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.

 

Answers (1)

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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