Question

Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...

Answer 1

In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,

`S_n = n/2[2a  + (n - 1)d]`

Where; a = first term for the given A.P.

d = common difference of the given A.P.

n = number of terms

2, 6, 10, 14, ... to 11 terms

Common difference of the A.P. (d) = `a_2 - a_1`

= 6 - 2

= 4

Number of terms (n) = 11

The first term for the given A.P. (a) = 2

So, using the formula we get,

`S_n = 11/2 [2(2) + (11 - 1)(4)]`

`= (11/2)[4 + (10)(4)]`

`= (11/2)[4 + 40]`

`= (11/2) [44]`

= 242

Therefore, the sum of first 11 terms for the given A.P. is 242