Aptitude 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**