Question

State whether True or False: In an AP, the sum of the first term and the last term is equal to the sum of the second term and the second last term and so on.

• A. True
• B. False

Answer 1

The correct option is A True

The sum of the first term and the last term are equal to the sum of the second term and the second last term and so on.

To show this, we can take up the general form of an AP with the terms as follows:
$\begin{array}{ccccccc}& & (a-d),& a& ,(a+d)& & \\ & (a-2d),& (a-d),& a& ,(a+d),& (a+2d)& \\ (a-3d),& (a-2d),& (a-d),& a& ,(a+d),& (a+2d),& (a+3d)\end{array}$

Observe that in each of the above arithmetic progressions, the sum of the first term and the last term is equal to the sum of the second term and the second last term and so on, which is “2a”.