Question

Find the sum of the following series

A. 144
B. 156
C. 168
D. 180

Answer 1

Lets rewrite the summation:

Summation from 1 to 12 of (2n+1) is equal to the summation of 1 to 12 of (2n) plus the summation from 1 to 12 of (1).

The summation from 1 to any number (
`n`) is given by:

`(n(n+1))/(2)`

So, the first term of our rewritten summation is equal to
`n(n+1)`.

The summation from 1 to any number (
`n`) of a constant (lets call it
`c`) is given by:


`nc`

So, the whole summation can be written as:

`n(n+1)+nc=n(n+1+c)`

For your problem we have
`n=12` and
`c=1`.

So, the answer is 168.