Question

The sum of a series of terms in A.P. is 128. If the first term is 2 and the last term is 14, find the common difference.

Answer 1

Let the number of terms in the series be $n$

Given that the sum of the series of terms in A.P. is $S_n=128$

Given that the first term is $a=2$

and last term is $a_n=14$

We know that the sum of the terms in A.P. is given by $S_n=\frac{n}{2}(a+a_n)$

$⟹128=\frac{n}{2}(2+14)$

$⟹\frac{n}{2}\left(16\right)=128$

$⟹n=16$

We know that $a_n=a+(n-1)d$

$⟹14=2+(16-1)d$

$⟹15d=12$

$⟹d=\frac{12}{15}=\frac{4}{5}$

Therefore, the common difference is $\frac{4}{5}$.