Arithmetic Sequence — Computing the Sum Sₙ — Dynamic Practice
Arithmetic Sequence — Computing the Sum Sₙ — Dynamic Practice. Practice questions to deepen understanding of computing the sum of the first n terms in an arithmetic sequence. Online math practice with full solutions and detailed explanations.
Dynamic practice in computing Sₙ — using Sₙ = n(a₁ + aₙ)/2 or Sₙ = n(2a₁ + (n−1)d)/2. New questions every attempt.
Question 1
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 17 terms \(S_{17}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 17 terms \(S_{17}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{17} = \frac{17(2 \cdot 9 + (17-1) \cdot 3)}{2}\)
\(S_{17} = \frac{17(18 + 48)}{2}\)
\(S_{17} = \frac{17 \cdot 66}{2} = \frac{1122}{2} = 561\)
\(S_{17} = \frac{17(18 + 48)}{2}\)
\(S_{17} = \frac{17 \cdot 66}{2} = \frac{1122}{2} = 561\)
Answer: 561
Question 2
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 4\)
Find the sum of the first 19 terms \(S_{19}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 4\)
Find the sum of the first 19 terms \(S_{19}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{19} = \frac{19(2 \cdot 4 + (19-1) \cdot 4)}{2}\)
\(S_{19} = \frac{19(8 + 72)}{2}\)
\(S_{19} = \frac{19 \cdot 80}{2} = \frac{1520}{2} = 760\)
\(S_{19} = \frac{19(8 + 72)}{2}\)
\(S_{19} = \frac{19 \cdot 80}{2} = \frac{1520}{2} = 760\)
Answer: 760
Question 3
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 4\)
Find the sum of the first 8 terms \(S_{8}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 4\)
Find the sum of the first 8 terms \(S_{8}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{8} = \frac{8(2 \cdot 1 + (8-1) \cdot 4)}{2}\)
\(S_{8} = \frac{8(2 + 28)}{2}\)
\(S_{8} = \frac{8 \cdot 30}{2} = \frac{240}{2} = 120\)
\(S_{8} = \frac{8(2 + 28)}{2}\)
\(S_{8} = \frac{8 \cdot 30}{2} = \frac{240}{2} = 120\)
Answer: 120
Question 4
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 11 terms \(S_{11}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 11 terms \(S_{11}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{11} = \frac{11(2 \cdot 9 + (11-1) \cdot 3)}{2}\)
\(S_{11} = \frac{11(18 + 30)}{2}\)
\(S_{11} = \frac{11 \cdot 48}{2} = \frac{528}{2} = 264\)
\(S_{11} = \frac{11(18 + 30)}{2}\)
\(S_{11} = \frac{11 \cdot 48}{2} = \frac{528}{2} = 264\)
Answer: 264
Question 5
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 3\)
Find the sum of the first 10 terms \(S_{10}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 3\)
Find the sum of the first 10 terms \(S_{10}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{10} = \frac{10(2 \cdot 3 + (10-1) \cdot 3)}{2}\)
\(S_{10} = \frac{10(6 + 27)}{2}\)
\(S_{10} = \frac{10 \cdot 33}{2} = \frac{330}{2} = 165\)
\(S_{10} = \frac{10(6 + 27)}{2}\)
\(S_{10} = \frac{10 \cdot 33}{2} = \frac{330}{2} = 165\)
Answer: 165
Question 6
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 2\)
Find the sum of the first 9 terms \(S_{9}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 2\)
Find the sum of the first 9 terms \(S_{9}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{9} = \frac{9(2 \cdot 9 + (9-1) \cdot 2)}{2}\)
\(S_{9} = \frac{9(18 + 16)}{2}\)
\(S_{9} = \frac{9 \cdot 34}{2} = \frac{306}{2} = 153\)
\(S_{9} = \frac{9(18 + 16)}{2}\)
\(S_{9} = \frac{9 \cdot 34}{2} = \frac{306}{2} = 153\)
Answer: 153
Question 7
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 3\)
Find the sum of the first 12 terms \(S_{12}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 3\)
Find the sum of the first 12 terms \(S_{12}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{12} = \frac{12(2 \cdot 8 + (12-1) \cdot 3)}{2}\)
\(S_{12} = \frac{12(16 + 33)}{2}\)
\(S_{12} = \frac{12 \cdot 49}{2} = \frac{588}{2} = 294\)
\(S_{12} = \frac{12(16 + 33)}{2}\)
\(S_{12} = \frac{12 \cdot 49}{2} = \frac{588}{2} = 294\)
Answer: 294
Question 8
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 1\)
Find the sum of the first 10 terms \(S_{10}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 1\)
Find the sum of the first 10 terms \(S_{10}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{10} = \frac{10(2 \cdot 7 + (10-1) \cdot 1)}{2}\)
\(S_{10} = \frac{10(14 + 9)}{2}\)
\(S_{10} = \frac{10 \cdot 23}{2} = \frac{230}{2} = 115\)
\(S_{10} = \frac{10(14 + 9)}{2}\)
\(S_{10} = \frac{10 \cdot 23}{2} = \frac{230}{2} = 115\)
Answer: 115
Question 9
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 2\)
Find the sum of the first 16 terms \(S_{16}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 2\)
Find the sum of the first 16 terms \(S_{16}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{16} = \frac{16(2 \cdot 9 + (16-1) \cdot 2)}{2}\)
\(S_{16} = \frac{16(18 + 30)}{2}\)
\(S_{16} = \frac{16 \cdot 48}{2} = \frac{768}{2} = 384\)
\(S_{16} = \frac{16(18 + 30)}{2}\)
\(S_{16} = \frac{16 \cdot 48}{2} = \frac{768}{2} = 384\)
Answer: 384
Question 10
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 1\)
Find the sum of the first 18 terms \(S_{18}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 1\)
Find the sum of the first 18 terms \(S_{18}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{18} = \frac{18(2 \cdot 8 + (18-1) \cdot 1)}{2}\)
\(S_{18} = \frac{18(16 + 17)}{2}\)
\(S_{18} = \frac{18 \cdot 33}{2} = \frac{594}{2} = 297\)
\(S_{18} = \frac{18(16 + 17)}{2}\)
\(S_{18} = \frac{18 \cdot 33}{2} = \frac{594}{2} = 297\)
Answer: 297
Question 11
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 1\)
Find the sum of the first 13 terms \(S_{13}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 1\)
Find the sum of the first 13 terms \(S_{13}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{13} = \frac{13(2 \cdot 9 + (13-1) \cdot 1)}{2}\)
\(S_{13} = \frac{13(18 + 12)}{2}\)
\(S_{13} = \frac{13 \cdot 30}{2} = \frac{390}{2} = 195\)
\(S_{13} = \frac{13(18 + 12)}{2}\)
\(S_{13} = \frac{13 \cdot 30}{2} = \frac{390}{2} = 195\)
Answer: 195
Question 12
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 1\)
Find the sum of the first 18 terms \(S_{18}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 1\)
Find the sum of the first 18 terms \(S_{18}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{18} = \frac{18(2 \cdot 7 + (18-1) \cdot 1)}{2}\)
\(S_{18} = \frac{18(14 + 17)}{2}\)
\(S_{18} = \frac{18 \cdot 31}{2} = \frac{558}{2} = 279\)
\(S_{18} = \frac{18(14 + 17)}{2}\)
\(S_{18} = \frac{18 \cdot 31}{2} = \frac{558}{2} = 279\)
Answer: 279
Question 13
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 1\)
Find the sum of the first 10 terms \(S_{10}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 1\)
Find the sum of the first 10 terms \(S_{10}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{10} = \frac{10(2 \cdot 3 + (10-1) \cdot 1)}{2}\)
\(S_{10} = \frac{10(6 + 9)}{2}\)
\(S_{10} = \frac{10 \cdot 15}{2} = \frac{150}{2} = 75\)
\(S_{10} = \frac{10(6 + 9)}{2}\)
\(S_{10} = \frac{10 \cdot 15}{2} = \frac{150}{2} = 75\)
Answer: 75
Question 14
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 2\)
Find the sum of the first 12 terms \(S_{12}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 2\)
Find the sum of the first 12 terms \(S_{12}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{12} = \frac{12(2 \cdot 4 + (12-1) \cdot 2)}{2}\)
\(S_{12} = \frac{12(8 + 22)}{2}\)
\(S_{12} = \frac{12 \cdot 30}{2} = \frac{360}{2} = 180\)
\(S_{12} = \frac{12(8 + 22)}{2}\)
\(S_{12} = \frac{12 \cdot 30}{2} = \frac{360}{2} = 180\)
Answer: 180
Question 15
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 2\)
Find the sum of the first 12 terms \(S_{12}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 2\)
Find the sum of the first 12 terms \(S_{12}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{12} = \frac{12(2 \cdot 8 + (12-1) \cdot 2)}{2}\)
\(S_{12} = \frac{12(16 + 22)}{2}\)
\(S_{12} = \frac{12 \cdot 38}{2} = \frac{456}{2} = 228\)
\(S_{12} = \frac{12(16 + 22)}{2}\)
\(S_{12} = \frac{12 \cdot 38}{2} = \frac{456}{2} = 228\)
Answer: 228
Question 16
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 5\)
Find the sum of the first 18 terms \(S_{18}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 5\)
Find the sum of the first 18 terms \(S_{18}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{18} = \frac{18(2 \cdot 7 + (18-1) \cdot 5)}{2}\)
\(S_{18} = \frac{18(14 + 85)}{2}\)
\(S_{18} = \frac{18 \cdot 99}{2} = \frac{1782}{2} = 891\)
\(S_{18} = \frac{18(14 + 85)}{2}\)
\(S_{18} = \frac{18 \cdot 99}{2} = \frac{1782}{2} = 891\)
Answer: 891
Question 17
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 3\)
Find the sum of the first 15 terms \(S_{15}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 3\)
Find the sum of the first 15 terms \(S_{15}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{15} = \frac{15(2 \cdot 2 + (15-1) \cdot 3)}{2}\)
\(S_{15} = \frac{15(4 + 42)}{2}\)
\(S_{15} = \frac{15 \cdot 46}{2} = \frac{690}{2} = 345\)
\(S_{15} = \frac{15(4 + 42)}{2}\)
\(S_{15} = \frac{15 \cdot 46}{2} = \frac{690}{2} = 345\)
Answer: 345
Question 18
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 15 terms \(S_{15}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 15 terms \(S_{15}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{15} = \frac{15(2 \cdot 9 + (15-1) \cdot 3)}{2}\)
\(S_{15} = \frac{15(18 + 42)}{2}\)
\(S_{15} = \frac{15 \cdot 60}{2} = \frac{900}{2} = 450\)
\(S_{15} = \frac{15(18 + 42)}{2}\)
\(S_{15} = \frac{15 \cdot 60}{2} = \frac{900}{2} = 450\)
Answer: 450
Question 19
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 5\)
Find the sum of the first 13 terms \(S_{13}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 5\)
Find the sum of the first 13 terms \(S_{13}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{13} = \frac{13(2 \cdot 8 + (13-1) \cdot 5)}{2}\)
\(S_{13} = \frac{13(16 + 60)}{2}\)
\(S_{13} = \frac{13 \cdot 76}{2} = \frac{988}{2} = 494\)
\(S_{13} = \frac{13(16 + 60)}{2}\)
\(S_{13} = \frac{13 \cdot 76}{2} = \frac{988}{2} = 494\)
Answer: 494
Question 20
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 4\)
Find the sum of the first 9 terms \(S_{9}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 4\)
Find the sum of the first 9 terms \(S_{9}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{9} = \frac{9(2 \cdot 2 + (9-1) \cdot 4)}{2}\)
\(S_{9} = \frac{9(4 + 32)}{2}\)
\(S_{9} = \frac{9 \cdot 36}{2} = \frac{324}{2} = 162\)
\(S_{9} = \frac{9(4 + 32)}{2}\)
\(S_{9} = \frac{9 \cdot 36}{2} = \frac{324}{2} = 162\)
Answer: 162
Question 21
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 2\)
Find the sum of the first 14 terms \(S_{14}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 2\)
Find the sum of the first 14 terms \(S_{14}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{14} = \frac{14(2 \cdot 8 + (14-1) \cdot 2)}{2}\)
\(S_{14} = \frac{14(16 + 26)}{2}\)
\(S_{14} = \frac{14 \cdot 42}{2} = \frac{588}{2} = 294\)
\(S_{14} = \frac{14(16 + 26)}{2}\)
\(S_{14} = \frac{14 \cdot 42}{2} = \frac{588}{2} = 294\)
Answer: 294
Question 22
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 3\)
Find the sum of the first 19 terms \(S_{19}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 3\)
Find the sum of the first 19 terms \(S_{19}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{19} = \frac{19(2 \cdot 1 + (19-1) \cdot 3)}{2}\)
\(S_{19} = \frac{19(2 + 54)}{2}\)
\(S_{19} = \frac{19 \cdot 56}{2} = \frac{1064}{2} = 532\)
\(S_{19} = \frac{19(2 + 54)}{2}\)
\(S_{19} = \frac{19 \cdot 56}{2} = \frac{1064}{2} = 532\)
Answer: 532
Question 23
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 5\)
• The common difference: \(d = 5\)
Find the sum of the first 11 terms \(S_{11}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 5\)
• The common difference: \(d = 5\)
Find the sum of the first 11 terms \(S_{11}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{11} = \frac{11(2 \cdot 5 + (11-1) \cdot 5)}{2}\)
\(S_{11} = \frac{11(10 + 50)}{2}\)
\(S_{11} = \frac{11 \cdot 60}{2} = \frac{660}{2} = 330\)
\(S_{11} = \frac{11(10 + 50)}{2}\)
\(S_{11} = \frac{11 \cdot 60}{2} = \frac{660}{2} = 330\)
Answer: 330
Question 24
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 2\)
Find the sum of the first 9 terms \(S_{9}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 2\)
Find the sum of the first 9 terms \(S_{9}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{9} = \frac{9(2 \cdot 2 + (9-1) \cdot 2)}{2}\)
\(S_{9} = \frac{9(4 + 16)}{2}\)
\(S_{9} = \frac{9 \cdot 20}{2} = \frac{180}{2} = 90\)
\(S_{9} = \frac{9(4 + 16)}{2}\)
\(S_{9} = \frac{9 \cdot 20}{2} = \frac{180}{2} = 90\)
Answer: 90
Question 25
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 5\)
Find the sum of the first 10 terms \(S_{10}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 5\)
Find the sum of the first 10 terms \(S_{10}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{10} = \frac{10(2 \cdot 1 + (10-1) \cdot 5)}{2}\)
\(S_{10} = \frac{10(2 + 45)}{2}\)
\(S_{10} = \frac{10 \cdot 47}{2} = \frac{470}{2} = 235\)
\(S_{10} = \frac{10(2 + 45)}{2}\)
\(S_{10} = \frac{10 \cdot 47}{2} = \frac{470}{2} = 235\)
Answer: 235
Question 26
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 4\)
Find the sum of the first 19 terms \(S_{19}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 4\)
Find the sum of the first 19 terms \(S_{19}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{19} = \frac{19(2 \cdot 8 + (19-1) \cdot 4)}{2}\)
\(S_{19} = \frac{19(16 + 72)}{2}\)
\(S_{19} = \frac{19 \cdot 88}{2} = \frac{1672}{2} = 836\)
\(S_{19} = \frac{19(16 + 72)}{2}\)
\(S_{19} = \frac{19 \cdot 88}{2} = \frac{1672}{2} = 836\)
Answer: 836
Question 27
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 4\)
Find the sum of the first 18 terms \(S_{18}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 4\)
Find the sum of the first 18 terms \(S_{18}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{18} = \frac{18(2 \cdot 7 + (18-1) \cdot 4)}{2}\)
\(S_{18} = \frac{18(14 + 68)}{2}\)
\(S_{18} = \frac{18 \cdot 82}{2} = \frac{1476}{2} = 738\)
\(S_{18} = \frac{18(14 + 68)}{2}\)
\(S_{18} = \frac{18 \cdot 82}{2} = \frac{1476}{2} = 738\)
Answer: 738
Question 28
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 4\)
Find the sum of the first 13 terms \(S_{13}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 4\)
Find the sum of the first 13 terms \(S_{13}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{13} = \frac{13(2 \cdot 3 + (13-1) \cdot 4)}{2}\)
\(S_{13} = \frac{13(6 + 48)}{2}\)
\(S_{13} = \frac{13 \cdot 54}{2} = \frac{702}{2} = 351\)
\(S_{13} = \frac{13(6 + 48)}{2}\)
\(S_{13} = \frac{13 \cdot 54}{2} = \frac{702}{2} = 351\)
Answer: 351
Question 29
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 5\)
Find the sum of the first 12 terms \(S_{12}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 5\)
Find the sum of the first 12 terms \(S_{12}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{12} = \frac{12(2 \cdot 9 + (12-1) \cdot 5)}{2}\)
\(S_{12} = \frac{12(18 + 55)}{2}\)
\(S_{12} = \frac{12 \cdot 73}{2} = \frac{876}{2} = 438\)
\(S_{12} = \frac{12(18 + 55)}{2}\)
\(S_{12} = \frac{12 \cdot 73}{2} = \frac{876}{2} = 438\)
Answer: 438
Question 30
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 8 terms \(S_{8}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 3\)
Find the sum of the first 8 terms \(S_{8}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{8} = \frac{8(2 \cdot 9 + (8-1) \cdot 3)}{2}\)
\(S_{8} = \frac{8(18 + 21)}{2}\)
\(S_{8} = \frac{8 \cdot 39}{2} = \frac{312}{2} = 156\)
\(S_{8} = \frac{8(18 + 21)}{2}\)
\(S_{8} = \frac{8 \cdot 39}{2} = \frac{312}{2} = 156\)
Answer: 156
Question 31
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 5\)
Find the sum of the first 12 terms \(S_{12}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 5\)
Find the sum of the first 12 terms \(S_{12}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{12} = \frac{12(2 \cdot 3 + (12-1) \cdot 5)}{2}\)
\(S_{12} = \frac{12(6 + 55)}{2}\)
\(S_{12} = \frac{12 \cdot 61}{2} = \frac{732}{2} = 366\)
\(S_{12} = \frac{12(6 + 55)}{2}\)
\(S_{12} = \frac{12 \cdot 61}{2} = \frac{732}{2} = 366\)
Answer: 366
Question 32
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 2\)
Find the sum of the first 16 terms \(S_{16}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 2\)
• The common difference: \(d = 2\)
Find the sum of the first 16 terms \(S_{16}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{16} = \frac{16(2 \cdot 2 + (16-1) \cdot 2)}{2}\)
\(S_{16} = \frac{16(4 + 30)}{2}\)
\(S_{16} = \frac{16 \cdot 34}{2} = \frac{544}{2} = 272\)
\(S_{16} = \frac{16(4 + 30)}{2}\)
\(S_{16} = \frac{16 \cdot 34}{2} = \frac{544}{2} = 272\)
Answer: 272
Question 33
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 5\)
Find the sum of the first 11 terms \(S_{11}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 5\)
Find the sum of the first 11 terms \(S_{11}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{11} = \frac{11(2 \cdot 4 + (11-1) \cdot 5)}{2}\)
\(S_{11} = \frac{11(8 + 50)}{2}\)
\(S_{11} = \frac{11 \cdot 58}{2} = \frac{638}{2} = 319\)
\(S_{11} = \frac{11(8 + 50)}{2}\)
\(S_{11} = \frac{11 \cdot 58}{2} = \frac{638}{2} = 319\)
Answer: 319
Question 34
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 1\)
Find the sum of the first 18 terms \(S_{18}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 1\)
Find the sum of the first 18 terms \(S_{18}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{18} = \frac{18(2 \cdot 9 + (18-1) \cdot 1)}{2}\)
\(S_{18} = \frac{18(18 + 17)}{2}\)
\(S_{18} = \frac{18 \cdot 35}{2} = \frac{630}{2} = 315\)
\(S_{18} = \frac{18(18 + 17)}{2}\)
\(S_{18} = \frac{18 \cdot 35}{2} = \frac{630}{2} = 315\)
Answer: 315
Question 35
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 3\)
Find the sum of the first 11 terms \(S_{11}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 4\)
• The common difference: \(d = 3\)
Find the sum of the first 11 terms \(S_{11}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{11} = \frac{11(2 \cdot 4 + (11-1) \cdot 3)}{2}\)
\(S_{11} = \frac{11(8 + 30)}{2}\)
\(S_{11} = \frac{11 \cdot 38}{2} = \frac{418}{2} = 209\)
\(S_{11} = \frac{11(8 + 30)}{2}\)
\(S_{11} = \frac{11 \cdot 38}{2} = \frac{418}{2} = 209\)
Answer: 209
Question 36
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 2\)
Find the sum of the first 10 terms \(S_{10}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 7\)
• The common difference: \(d = 2\)
Find the sum of the first 10 terms \(S_{10}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{10} = \frac{10(2 \cdot 7 + (10-1) \cdot 2)}{2}\)
\(S_{10} = \frac{10(14 + 18)}{2}\)
\(S_{10} = \frac{10 \cdot 32}{2} = \frac{320}{2} = 160\)
\(S_{10} = \frac{10(14 + 18)}{2}\)
\(S_{10} = \frac{10 \cdot 32}{2} = \frac{320}{2} = 160\)
Answer: 160
Question 37
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 5\)
Find the sum of the first 15 terms \(S_{15}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 3\)
• The common difference: \(d = 5\)
Find the sum of the first 15 terms \(S_{15}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{15} = \frac{15(2 \cdot 3 + (15-1) \cdot 5)}{2}\)
\(S_{15} = \frac{15(6 + 70)}{2}\)
\(S_{15} = \frac{15 \cdot 76}{2} = \frac{1140}{2} = 570\)
\(S_{15} = \frac{15(6 + 70)}{2}\)
\(S_{15} = \frac{15 \cdot 76}{2} = \frac{1140}{2} = 570\)
Answer: 570
Question 38
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 2\)
Find the sum of the first 17 terms \(S_{17}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 8\)
• The common difference: \(d = 2\)
Find the sum of the first 17 terms \(S_{17}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{17} = \frac{17(2 \cdot 8 + (17-1) \cdot 2)}{2}\)
\(S_{17} = \frac{17(16 + 32)}{2}\)
\(S_{17} = \frac{17 \cdot 48}{2} = \frac{816}{2} = 408\)
\(S_{17} = \frac{17(16 + 32)}{2}\)
\(S_{17} = \frac{17 \cdot 48}{2} = \frac{816}{2} = 408\)
Answer: 408
Question 39
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 1\)
Find the sum of the first 11 terms \(S_{11}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 1\)
• The common difference: \(d = 1\)
Find the sum of the first 11 terms \(S_{11}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{11} = \frac{11(2 \cdot 1 + (11-1) \cdot 1)}{2}\)
\(S_{11} = \frac{11(2 + 10)}{2}\)
\(S_{11} = \frac{11 \cdot 12}{2} = \frac{132}{2} = 66\)
\(S_{11} = \frac{11(2 + 10)}{2}\)
\(S_{11} = \frac{11 \cdot 12}{2} = \frac{132}{2} = 66\)
Answer: 66
Question 40
2.50 pts
📊 Arithmetic Sequence:
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 4\)
Find the sum of the first 8 terms \(S_{8}\).
Given an arithmetic sequence where:
• First term: \(a_1 = 9\)
• The common difference: \(d = 4\)
Find the sum of the first 8 terms \(S_{8}\).
Explanation:
Solution – Arithmetic Sequence:
📝 Important formulas:
\(a_n = a_1 + (n-1) \cdot d\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_n = \frac{n(a_1 + a_n)}{2} = \frac{n(2a_1 + (n-1)d)}{2}\)
🔢 Solution:
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
We will use the formula: \(S_n = \frac{n(2a_1 + (n-1)d)}{2}\)
\(S_{8} = \frac{8(2 \cdot 9 + (8-1) \cdot 4)}{2}\)
\(S_{8} = \frac{8(18 + 28)}{2}\)
\(S_{8} = \frac{8 \cdot 46}{2} = \frac{368}{2} = 184\)
\(S_{8} = \frac{8(18 + 28)}{2}\)
\(S_{8} = \frac{8 \cdot 46}{2} = \frac{368}{2} = 184\)
Answer: 184