Question

Find the sum of n terms of the series whose nth term are given below
4n^3+6n^2+2n+3

Answer 1

Step-by-step explanation:

Nth term, An is

$4 {n}^{3} + 6 {n}^{2} + 2n + 3$

Also,

An= A1+(n-1)d

A1= An-(n-1)d

Now, Sum of series

$Sn = \frac{n}{2} (A1+An) \\ Sn = \frac{n}{2} (An - (n - 1)d+An) \\ Sn = \frac{n}{2} (2An - (n - 1)d) \\ Sn = \frac{n}{2} (2(4 {n}^{3} + 6 {n}^{2} + 2n + 3)- (n - 1)d) \\ Sn = \frac{n}{2} (8 {n}^{3} + 12{n}^{2} + 4n + 6- nd + d)$