Question

In an A.P., if the common difference is $2$ and sum up to $n$ terms is $49$ and $7^{th}$ term is $13$, then value of $n$ is equal to?

• A. $0$
• B. $5$
• C. $7$
• D. $13$

Answer 1

Answer: (C)

$7$

Given: $a_7=a_1+6d$

It is given that the common difference is 2.

Therefore

$a_7=a_1+12$

$13=a_1+12$
$a_1=1$.

Now sum of n terms is given by:

$S_n=\frac{n}{2}[2a_1+(n-1\left)d\right]$

$49=\frac{n}{2}[2+(n-1\left)2\right]$

$49=n(1+(n-1\left)\right)$

$49=n^2$

$n=7$

Hence the value of n is 7.