What is the sum of the first 15 terms of the arithmetic progression (2, 7, 12, 17, …)?
Answer and explanation
Correct answer: 555
Apply the AP sum formula Sₙ = n/2 [2a₁ + (n − 1)d]. Here a₁ = 2, d = 7 − 2 = 5, and n = 15. Therefore S₁₅ = 15/2 [2(2) + 14(5)] = 15/2 [4 + 70] = 15/2 × 74 = 15 × 37 = 555. A second check gives the fifteenth term a₁₅ = 2 + 14 × 5 = 72, so S₁₅ = 15/2(2 + 72) = 555. The distractors arise from an incorrect term count or arithmetic simplification. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
555
Why is this the correct answer?
Apply the AP sum formula Sₙ = n/2 [2a₁ + (n − 1)d]. Here a₁ = 2, d = 7 − 2 = 5, and n = 15. Therefore S₁₅ = 15/2 [2(2) + 14(5)] = 15/2 [4 + 70] = 15/2 × 74 = 15 × 37 = 555. A second check gives the fifteenth term a₁₅ = 2 + 14 × 5 = 72, so S₁₅ = 15/2(2 + 72) = 555. The distractors arise from an incorrect term count or arithmetic simplification. Hence option B 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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