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  • Tell me? If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

  • Option 1)

    \left ( -\infty ,-10 \right )

     

     

     

  • Option 2)

    \left ( -10 ,0 \right )

  • Option 3)

    \left ( 0 ,10 \right )

  • Option 4)

    \left ( 10 ,\infty \right )

 

Answers (3)

best_answer

As we learned

 

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

 

 \int_{\infty }= \frac{a}{1-r}\; \; \; ;\; \; \; \left | r \right |< 1\: \: \: \: \: \: ;r\neq 0

\frac{b}{1-r}=5\Rightarrow b=5-5r

also  -1< r< 1

-5< 5r< 5

0< 5-5r< 10

 


Option 1)

\left ( -\infty ,-10 \right )

 

 

 

Option 2)

\left ( -10 ,0 \right )

Option 3)

\left ( 0 ,10 \right )

Option 4)

\left ( 10 ,\infty \right )

Posted by

Himanshu

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Posted by

K.srikar

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