Question

The sum of the first n terms of an AP is given by Sn=3n^2+6n.find the nth term of this AP

Answer 1

Sn = 3n²+6n

S1 = a1 = 3 + 6 = 9

S2 = 3X4 + 6X2 = 24

a1 + a2 = S2
 therefore, a2 = 24 - 9 = 15

d = a2 - a1 = 15 - 9 = 6

an = a + (n-1)d = 9 +(n-1) 6 = 9 + 6n - 6 = 3 + 6n = 3(1+2n)