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5. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

5. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
Given that, first term, a = 5 last term, l = 45 Sum of the AP, Sn = 400 As we know, the sum of AP formula is; Sn = n/2 (a+l) 400 = n/2(5+45) 400 = n/2(50) Number of terms, n =16 As we know, the last term of AP series can be written as; l = a+(n −1)d 45 = 5 +(16 −1)d 40 = 15d Common difference, d = 40/15 = 8/3

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