8. Sequences and Series
medium

किसी गुणोत्तर श्रेणी का चौथा पद उसके दूसरे पद का वर्ग है तथा प्रथम पद $-3$ है तो $7$ वाँ पद ज्ञात कीजिए।

A

$-2187$

B

$-2187$

C

$-2187$

D

$-2187$

Solution

Let $a$ be the first term and $r$ be the common ratio of the $G.P. $

$\therefore a=-3$

It is known that, $a_{n}=a r^{n-1}$

$\therefore a_{4}=a r^{3}=(-3) r^{3}$

$a_{2}=a r^{2}=(-3) r$

According to the given condition,

$(-3) r^{3}=[(-3) r]^{2}$

$\Rightarrow-3 r^{3}=9 r^{2} \Rightarrow r=-3 a_{7}=a r^{7-1}=a r^{6}=(-3)(-3)^{6}=-(3)^{7}=-2187$

Thus, the seventh term of the $G.P.$ is $-2187 .$

Standard 11
Mathematics

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