Question

The sum of the first n terms of an Ap is 3n²+6n. Find the nth term and 15th term?​

Answer 1

Answer:

The nth term is 3 + 6 n and the 15th term is 93

Step-by-step explanation:

Given : S n = 3 n^2 + 6 n

S n = n/2( 2 a + (n-1)d)

equating both sides:

3 n^2 + 6 n = n/2(2 a + (n-1)d)

2(3 n^2 + 6 n)/n =  2 a + (n-1)d

6 n + 12 = 2 a + d n - d  

Comparing the sides:

6 n = d n

Therefore d = 6

2 a - d = 12

2 a - 6 = 12

2 a = 18

a = 9

So the nth term will be:

An = a + (n-1)d

An = 9 + (n-1)6

     = 9 + 6 n - 6

     = 3 + 6 n

And the 15th term will be:

A_15 = 3 + 6 x 15

        = 3 + 90 = 93

Answer 2

Refers to attachment ♡~