# Choose the correct answer from the given four options:If the $2^{\text {nd }}$ term of an AP is 13 and the $5^{\text {th }}$ term is 25 , what is its $7^{\text {th }}$ term?(A) 30(B) 33(C) 37(D) 38

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Given:

The $2^{nd}$ term of an A.P. is $13$ and the $5^{th}$ term is $25$.

To do:

We have to find $7^{th}$ term.

Solution:

Let $a$ be the first term and $d$ be the common difference of the A.P.

As we know,

$a_n=a+( n-1)d$

$\Rightarrow 2^{nd}$ term $a_2=a+( 2-1)d$

$\Rightarrow 13=a+d\ ........\ ( i)$

Similarly, $5^{th}$ term $a_5=a+( 5-1)d$

$25=a+4d\ ........\ ( ii)$

On substracting $( i)$ from $( ii)$

$a+4d-a-d=25-13$

$\Rightarrow 3d=12$

$\Rightarrow d=\frac{12}{3}$

$\Rightarrow d=4$

On substituting $d=4$ in $( i)$

$a+4=13$

$\Rightarrow a=13-4=9$

Therefore, $7^{th}$ term of the A.P. , $a_7=9+( 7-1)4$

$=9+24$

$=33$

Thus, $7^{th}$ term of the A.P. is $33$.

Updated on 10-Oct-2022 13:27:27