What is the sum of the first 8 terms of the arithmetic progression (3, 8, 13, 18, …)?
Answer and explanation
Correct answer: 164
The governing idea is the finite-sum formula for an arithmetic progression, Sₙ = n/2 [2a₁ + (n − 1)d]. The first term is a₁ = 3, the common difference is d = 8 − 3 = 5, and n = 8. Substitution gives S₈ = 8/2 [2(3) + 7(5)] = 4[6 + 35] = 4 × 41 = 164. As a verification, the eighth term is a₈ = 3 + 7 × 5 = 38; pairing the first and last terms gives S₈ = 8/2(3 + 38) = 4 × 41 = 164. The other choices do not satisfy this calculation. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
164
Why is this the correct answer?
The governing idea is the finite-sum formula for an arithmetic progression, Sₙ = n/2 [2a₁ + (n − 1)d]. The first term is a₁ = 3, the common difference is d = 8 − 3 = 5, and n = 8. Substitution gives S₈ = 8/2 [2(3) + 7(5)] = 4[6 + 35] = 4 × 41 = 164. As a verification, the eighth term is a₈ = 3 + 7 × 5 = 38; pairing the first and last terms gives S₈ = 8/2(3 + 38) = 4 × 41 = 164. The other choices do not satisfy this calculation. Thus option C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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