What is the sum of the first 15 terms of the arithmetic progression (2, 7, 12, 17, …)?
Answer and explanation
Correct answer: 555
Direct answer: B, 555. In the AP, the first term is a=2, the common difference is d=7−2=5, and the number of terms is n=15. Use Sₙ=n/2[2a+(n−1)d]. Therefore S₁₅=15/2[2(2)+14(5)]=15/2(4+70)=15/2×74=15×37=555. A second check uses the last term: a₁₅=a+(15−1)d=2+14×5=72. In an AP, the average of the first and last terms is (2+72)/2=37, so the sum is 15×37=555. A, 545, C, 560, and D, 570, do not agree with either calculation. The common error is using 15d instead of 14d for the fifteenth term; there are fourteen equal gaps from the first to the fifteenth term.
Frequently asked questions
What is the correct answer to this question?
555
Why is this the correct answer?
Direct answer: B, 555. In the AP, the first term is a=2, the common difference is d=7−2=5, and the number of terms is n=15. Use Sₙ=n/2[2a+(n−1)d]. Therefore S₁₅=15/2[2(2)+14(5)]=15/2(4+70)=15/2×74=15×37=555. A second check uses the last term: a₁₅=a+(15−1)d=2+14×5=72. In an AP, the average of the first and last terms is (2+72)/2=37, so the sum is 15×37=555. A, 545, C, 560, and D, 570, do not agree with either calculation. The common error is using 15d instead of 14d for the fifteenth term; there are fourteen equal gaps from the first to the fifteenth term.
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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