# Fifth term of an GP is 2, then the product of its 9 terms is Option 1) $256$ Option 2) $512$ Option 3) $1024$ Option 4) none.

As we learnt in

Common ratio of a GP (r) -

The ratio of two consecutive terms of a GP

- wherein

eg: in 2, 4, 8, 16, - - - - - - -

r = 2

and in 100, 10, 1, 1/10 - - - - - - -

r = 1/10

Given $ar^{4}= 2$

Now

$\Rightarrow a\times ar\times ar^{2}\times \cdot \cdot \cdot ar^{8}$

$= a^{9}\cdot r^{1=2+3+....8}$

$= a^{9}\cdot r\tfrac{8\times 9}{2}= a^{9}r^{36}= \left ( ar^{4} \right )^{9}= 2^{9}= 512$

Option 1)

$256$

This option is incorrect.

Option 2)

$512$

This option is correct.

Option 3)

$1024$

This option is incorrect.

Option 4)

none.

This option is incorrect.

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