Question

If the sum of the first n terms of an A.P. is given by `S_n = n/2 (3n + 1)`, then the first term of the A.P. is ______.

Options

• 2

• `3/2`

• 4

• `5/2`

Answer 1

If the sum of the first n terms of an A.P. is given by `S_n = n/2 (3n + 1)`, then the first term of the A.P. is 2.

Explanation:

Given, `S_n = n/2 (3n + 1)`

For n = 1

`S_1 = 1/2 (3 xx 1 + 1)`

`S_1 = 1/2 xx 4`

S₁ = 2

S₁ = a = 2

Hence, the first term of the A.P. is 2.