Sum of infinite number of terms in GP is 20 and sum of their square is 100. The common ratio of GP is

  • Option 1)

    5

  • Option 2)

    3/5

  • Option 3)

    8/5

  • Option 4)

    1/5

 

Answers (1)

As we learnt in

Sum of infinite terms of a GP -

a+ar+ar^{2}+- - - - -= \frac{a}{1-r}\\here \left | r \right |<1

- wherein

a\rightarrow first term

r\rightarrow common ratio

 

Let the GP be 

a_{1}ar_{1}ar^{2}\cdot \cdot \infty

S_{\infty }=\frac{a}{1-r}=20

\Rightarrow \left ( \frac{a}{1-r} \right )^{2}= 400                   (i)

Similarly

S_{\infty }= \frac{a^{2}}{1-r^{2}} = 100                      (ii)

\frac{eg \left ( i\right )}{eg\left ( ii \right )}= \frac{a^{2}}{\left ( 1-r \right )^{2}}\times \frac{1-r^{2}}{a^{2}}= \frac{400}{100}= 4

= \frac{\left ( 1-r \right )\left ( 1+r \right )}{\left ( 1-r \right )\left ( 1-r \right )}= 4

\Rightarrow 1+r= 4-4r

5r=3

r= \frac{3}{5} 


Option 1)

5

This option is incorrect.

Option 2)

3/5

This option is correct.

Option 3)

8/5

This option is incorrect.

Option 4)

1/5

This option is incorrect.

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