Question

The sum of first $10$ terms and $20$ terms of an AP are $120$ and $440$ respectively. What is the common difference?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

Let the first term be $a$ and common difference be $d$.
Sum of first n terms in an A.P. $=\frac{n}{2}(2a+(n-1\left)d\right)$

So, sum of first $10$ terms $=\frac{10}{2}(2a+(10-1\left)d\right)$

$⟹120=5(2a+9d)$

$⟹24=2a+9d$ .............. $\left(i\right)$
Sum of first 20 terms $=\frac{20}{2}(2a+(20-1\left)d\right)$

$⟹440=10(2a+19d)$

$⟹44=2a+19d$ ......... $\left(ii\right)$
Subtracting equation (i) from (ii) gives
$20=10d$
$⟹d=2$
Common difference =2

Hence, option B is correct.