What is the sum of the first 9 terms of the arithmetic progression (8, 14, 20, 26, …)?
Answer and explanation
Correct answer: 288
Use the arithmetic-progression sum formula Sₙ = n/2[2a + (n − 1)d]. The first term is a = 8, the common difference is d = 14 − 8 = 6, and n = 9. Hence S₉ = 9/2[2(8) + 8(6)] = 9/2[16 + 48] = 9/2 × 64 = 288. Therefore, option B is correct. As a verification, the ninth term is a₉ = 8 + 8 × 6 = 56, and pairing the first and last terms gives 9(8 + 56)/2 = 288. Options A, C, and D can arise from using an incorrect difference, miscounting the eight intervals, or making an addition or multiplication error.
Frequently asked questions
What is the correct answer to this question?
288
Why is this the correct answer?
Use the arithmetic-progression sum formula Sₙ = n/2[2a + (n − 1)d]. The first term is a = 8, the common difference is d = 14 − 8 = 6, and n = 9. Hence S₉ = 9/2[2(8) + 8(6)] = 9/2[16 + 48] = 9/2 × 64 = 288. Therefore, option B is correct. As a verification, the ninth term is a₉ = 8 + 8 × 6 = 56, and pairing the first and last terms gives 9(8 + 56)/2 = 288. Options A, C, and D can arise from using an incorrect difference, miscounting the eight intervals, or making an addition or multiplication error.
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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