Question

In an A.P. the sum of terms equidistant from the beginning and end is equal to ?

Answer 1

We know the formula for the sum of an A.P. series:

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Here, n=number of terms

a=first term

d=common difference

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]=\frac{n}{2}\left[\right(a)+(a+(n-1)d\left)\right]$

So, the sum of the series is equal to the product of the sum of the first and last terms and the half of the total no. of terms.