Question:
The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7th term.
Solution:
Let $r$ be the common ratio of the given G.P.'
Then, $a_{4}=\left(a_{2}\right)^{2}$ [Given]
Now, $a r^{3}=a^{2} r^{2}$
$\Rightarrow r=a$
$\Rightarrow r=-3$ [Putting $a=-3$ ]
$\therefore a_{7}=a r^{6}$
$\Rightarrow a_{7}=(-3)(-3)^{6}$ [Putting $a=-3$ and $r=-3$ ]
$\Rightarrow a_{7}=(-3)(-729)$
$\Rightarrow a_{7}=-2187$
Thus, the $7^{\text {th }}$ term of the G.P. is $-2187$.