If the fifth term of a G.P. is 2, then write the product of its 9 terms.

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 $=2^{9}=512$

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