Question

If the sum of 16 terms of an arithmetic progression is 1624 and the first term is 500 times the common difference, then find the common difference.

• A. $\frac{1}{5}$
• B. $\frac{2}{3}$
• C. $\frac{3}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is A $\frac{1}{5}$

Let $a$ be the first term and $d$ be their common difference of the AP.

Then, Sum to $n$ terms of an AP $=\frac{n}{2}(2a+(n-1\left)d\right)$

Here, in the given AP,. $a=500d$

Given,$S_{16}=1624$

$=>\frac{16}{2}\left(2\right(500d)+(16-1\left)\right(d\left)\right)=1624$

$=>8(1000d+15d)=1624$

$=>1015d=203$

$=>d=\frac{1}{5}$