Question

Sum of first $25$ terms of an AP is $525$. Sum of the next $25$ terms is $725$. What is the common difference?

• A. $\frac{8}{25}$
• B. $\frac{4}{25}$
• C. $\frac{6}{25}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$\frac{8}{25}$

The sum of the first $25$ terms, $S_{25}=525$
The sum of the next $25$ terms, $K_{25}=$ sum of next $25$ terms $=725$

$K_{25}=a_{26}+a_{27}+.........a_{50}$

$K_{25}=a_1+25d+a_2+25d+..........a_{25}+25d$

$\Rightarrow K_{25}=a_1+a_2.......a_{25}+625d$

So, $K_{25}=S_{25}+25\times 25d$

i.e $725=525+25\times 25d$

$200=25\times 25d$

$\therefore d=\frac{8}{25}$