What is the sum of the first 8 terms of the arithmetic progression (3, 8, 13, 18, …)?
Answer and explanation
Correct answer: 164
Direct answer: option C, 164. In an arithmetic progression (AP), each term changes by the same common difference. Here the first term is a = 3, the common difference is d = 8 − 3 = 5, and the number of terms is n = 8. Use Sₙ = n/2[2a + (n − 1)d]. Thus S₈ = 8/2[2(3) + 7(5)] = 4(6 + 35) = 164. A useful check is to find the eighth term: a₈ = 3 + 7(5) = 38. The average of the first and last terms is (3 + 38)/2 = 20.5, so the sum is 8 × 20.5 = 164. A (156) is too small, B (160) does not result from the formula, and D (168) is too large. Remember: for n terms, use n − 1 differences, not n differences.
Frequently asked questions
What is the correct answer to this question?
164
Why is this the correct answer?
Direct answer: option C, 164. In an arithmetic progression (AP), each term changes by the same common difference. Here the first term is a = 3, the common difference is d = 8 − 3 = 5, and the number of terms is n = 8. Use Sₙ = n/2[2a + (n − 1)d]. Thus S₈ = 8/2[2(3) + 7(5)] = 4(6 + 35) = 164. A useful check is to find the eighth term: a₈ = 3 + 7(5) = 38. The average of the first and last terms is (3 + 38)/2 = 20.5, so the sum is 8 × 20.5 = 164. A (156) is too small, B (160) does not result from the formula, and D (168) is too large. Remember: for n terms, use n − 1 differences, not n differences.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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