Question

the sum of the first n term of an ap is 3n square + 6n find the nth term of this AP

Answer 1

Let sn denotes the sum of n terms of the AP.whose nth term is an.

an = sn - s(n-1)

     = (3n^2 + 6n) - (3(n-1)^2 + 6(n-1))

     = 3n^2 + 6n - (3(n^2 + 1 - 2n) + 6(n - 1))

     = 3n^2 + 6n - (3n^2 + 3 - 6n) + 6n - 6

    = 3n^2 + 6n - 3n^2 - 3 + 6n - 6n + 6

    = 6n + 3.

Therefore nth term an = 6n + 3.