Algebra
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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

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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


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