Question

If the sum of n terms of an A.P. is 2n² + 5n, then its nth term is

Options

• 4n − 3

• 3n − 4

• 4n + 3

• 3n + 4

Answer 1

Here, the sum of first n terms is given by the expression,

S_n = 2n² + 5n

We need to find the n^th term.

So we know that the n^thterm of an A.P. is given by,

a_n = S_n - S_n-1

So,

`a_n = (2n^2 + 5n) - [2(n-1)^2 + 5 (n-1)]`

Using the property,

( a - b)² = a² + b² - 2ab

We get,

`a_n = (2n^2 + 5n) - [2(n^2 + 1 - 2n) + 5 (n-1)]`

      = (2n² + 5n) +- (2n² + 2 - 4n + 5n - 5)

      = 2n² + 5n - 2n² - 2 + 4n - 5n + 5

      = 4n + 3 

Therefore, a_n = 4n + 3