Find the sum of the following series a. 144 b. 156 c. 168 d. 180

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 () is given by:


So, the first term of our rewritten summation is equal to .

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



So, the whole summation can be written as:


For your problem we have and .

So, the answer is 168.

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