# Moderate Algebra Solved QuestionAptitude Discussion

 Q. In an $A.P$, the $12^{th}$ term is 7 times the $2^{nd}$ term and the $8^{th}$ term is 3 more than 10 times the first term. What is the $5^{th}$ term of the $G.P$ whose first term is the first term of $A.P$ and whose common ratio is equal to the common difference of the $A.P$.
 ✔ A. 162 ✖ B. 144 ✖ C. 156 ✖ D. 136

Solution:
Option(A) is correct

Let the progression be $a,a+d,a+2d$ .........

$⇒ a+11d=7a+7d$

$⇒ 6a=4d$

$⇒ 3a=2d$

Also, $a+7d=10a+3$

$⇒ 7d=9a+3$

$⇒ 7d=6d+3$

$⇒ d=3,a=2$

The $GP$ is $2,2×3,2×32,2×33,2×34$

So the $5^{th}$ term is 162