Question

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

Answer 1

Let the first term of the AP be a, and the common difference be $d$. It is given that the $2^{nd}$ term is $13$ ie $t_2=a+d$ and also that the $5^{th}$ term is $25$, i.e. $t_5=a+4d$

Solving for $d$, we get

$(a+4d)-(a+d)=25-13=12$

Thus, $3d=12$

Or, $d=4$.

Hence, $a=13-4=9$. To find the $7^{th}$ term, we need to find the value of $a+6d$ i.e. $9+6\left(4\right)=33$.

Thus the $7^{th}$ term of the given arithmetic progression is $33$.