Question

Can the sum of n terms in an A. P. Is n square +13n .justify your answer

Answer 1

yes , sum of n terms of an AP would be n² + 13nwhose first term is 14 and common difference is 2.we have to check sum of n terms in an AP would be n² + 13n or not .let's try to resolve it in standard form of formula of sum of n terms.i.e.,

Sn = n/2[2a + (n - 1)d ] .......(1)

n² + 13n = n(n + 13)= n/2 (2n + 26)= n/2 [2n - 2 + 28 ]= n/2 [ 2(n - 1) + 2 × 14 ]= n/2 [2(14) + (n - 1)2 ]........(2)

on comparing equations (1) and (2) we see a = 14 and d = 2 {a and d are both integers }hence sum of n terms of an AP would be n² + 13nwhose first term is 14 and common difference is 2.

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