Question

If the $2^{nd}$ term of an AP is $13$ and the $5^{th}$ term is $25,$ what is its $7^{th}$ term?

• A. $30$
• B. $33$
• C. $37$
• D. $38$

Answer 1

The correct option is B $33$

Let the first term of the AP be $a$, the common difference be $d$.
Then,
$2^{nd}$ term is $a+d=\mathrm{13.......}\left(1\right)$
$5^{th}$ term is $a+4d=\mathrm{25........}\left(2\right)$

Solving for $d$,

By $Eq\left(2\right)-Eq\left(1\right)$
$(a+4d)-(a+d)=25-13$
$\Rightarrow 3d=12$
$\Rightarrow d=4$

Hence, From $\left(1\right)$

$a=13-d=13-4=9$

Now, $7^{th}$ term is $a+6d$

Substituting values of $a$ and $d$
$7^{th}term=9+6\times 4=33$