Question:
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
Solution:
Here, $a_{5}=2$
$\Rightarrow a r^{4}=2$
Product of the nine terms, i.e. $a, a r, a r^{2}, a r^{3}, a r^{4}, a r^{5}, a r^{6}, a r^{7}$ and $a r^{8}$ :
$\left(a \times a r^{8}\right)\left(a r \times a r^{7}\right)\left(a r^{2} \times a r^{6}\right)\left(a r^{3} \times a r^{5}\right)\left(a r^{4}\right)=\left(a r^{4}\right)^{9}$
$\because a r^{4}=2$
Required product $=2^{9}=512$