$\begin{array}{1 1}-2187 \\ 2187 \\ -1183 \\ -2347 \end{array} $

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- $n^{th}\:term$ of a G.P.$=a.r^{n-1}$ where $1^{st}\:term=a$ and $common\: ratio=r$

Given: In a G.P. $4^{th}\:term=(2^{nd}\:term)^2\:\:and 1^{st}\:term=-3$

$i.e., \:t_4=(t_2)^2\:\;and\:\:a=-3$

We know that $t_n=a.r^{n-1}$

$\therefore\:a.r^{4-1}=(a.r^{2-1})^2$

$\Rightarrow\:a.r^3=a^2.r^2$

$r=a$

Substituting the value of $a=r=-3$ we get

$t_7=a.r^{7-1}=a.r^6=-3.(-3)^6=-3^7=-2187$

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