The 4th term of a G.P. is square of its second term, and the first term is − 3.

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 $-2187$.

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