If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is

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Here, the sum of first n terms is given by the expression, Sn = 2n2 + 5n We need to find the nth term. So we know that the nthterm of an A.P. is given by, an = Sn - Sn-1 So, `a_n = (2n^2 + 5n) - [2(n-1)^2 + 5 (n-1)]` Using the property, ( a - b)2 = a2 + b2 - 2ab We get, `a_n = (2n^2 + 5n) - [2(n^2 + 1 - 2n) + 5 (n-1)]` = (2n2 + 5n) +- (2n2 + 2 - 4n + 5n - 5) = 2n2 + 5n - 2n2 - 2 + 4n - 5n + 5 = 4n + 3 Therefore, an = 4n + 3

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