If the 5th term of a GP is 2, find the product of its first nine terms.
Question:

If the $\mathbf{5}^{\text {th }}$ term of a GP is 2, find the product of its first nine terms.

Solution:

Given: $5^{\text {th }}$ term of a GP is $2 .$

To find: the product of its first nine terms.

First term is denoted by a, the common ratio is denote by r.

$\therefore a r^{4}=2$

We have to find the value of: $a \times a r^{1} \times a r^{2} \times a r^{3} \times \ldots \times a r^{8}$

$=a^{9} r^{1+2+3+4+\ldots+8}$

$=a^{9} r^{36}$

$=\left(a r^{4}\right)^{9}$

$=(2)^{9}$

$=512$

Ans: 512.