What is the sum of the first 16 terms of the arithmetic progression (4, 9, 14, 19, …)?
Answer and explanation
Correct answer: 664
Apply Sₙ = n/2[2a + (n − 1)d]. Here a = 4, d = 9 − 4 = 5, and n = 16. Thus S₁₆ = 16/2[2(4) + 15(5)] = 8[8 + 75] = 8 × 83 = 664. Therefore, option B is correct. A second check uses the last term: a₁₆ = 4 + 15 × 5 = 79, so the average of the first and last terms is (4 + 79)/2 = 41.5 and the sum is 16 × 41.5 = 664. The other choices reflect small arithmetic mistakes, such as using 14 instead of 15 intervals or miscalculating the bracket.
Frequently asked questions
What is the correct answer to this question?
664
Why is this the correct answer?
Apply Sₙ = n/2[2a + (n − 1)d]. Here a = 4, d = 9 − 4 = 5, and n = 16. Thus S₁₆ = 16/2[2(4) + 15(5)] = 8[8 + 75] = 8 × 83 = 664. Therefore, option B is correct. A second check uses the last term: a₁₆ = 4 + 15 × 5 = 79, so the average of the first and last terms is (4 + 79)/2 = 41.5 and the sum is 16 × 41.5 = 664. The other choices reflect small arithmetic mistakes, such as using 14 instead of 15 intervals or miscalculating the bracket.
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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