# the first n terms of an ap is 3n²+6n. Find the nth term of this ap

Sum of first n terms of AP, Sn = 3n^2 + 6n

Now choose n=1 and put in the above formula,

First term = 3+6 = 9

Now put n=2 to get the sum of first two terms = 3×4 + 6×2 = 12 + 12 = 24

This means

first term + second term = 24

but first term = 9 as calculated above

so, second term = 24 – 9 = 15

So common difference becomes, 15-9 = 6

So the AP becomes, 9, 15, 21, ….

nth term = a + (n – 1)d = 9 + (n-1)6 = 9 + 6n – 6 = 3 + 6n

Hence, nth term of given AP is (3 + 6n)