In an infinite Geomatric progression ,each term is equal to twice the sum of all the terms that follow it. if the sum of first two terms is 12, the sum of entire progression is

  • Option 1)

    \frac{9}{2}

  • Option 2)

    \frac{27}{2}

  • Option 3)

    \frac{88}{7}

  • Option 4)

    15

 

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

 

 Given

\\a=2\left ( ar+ar^{2+} +ar^{3}+........\infty \right )\\*\\* Thus, 1=\frac{2r}{1-r}\\*\\*1-r=2r\\*\\r=\frac{1}{3}

Also a+ar=12

4a/3=12

a=9

So, S_\infty =\frac{a}{1-r}=\frac{9}{1-\frac{1}{3}}=\frac{27}{2}


Option 1)

\frac{9}{2}

Incorrect

Option 2)

\frac{27}{2}

Correct

Option 3)

\frac{88}{7}

Incorrect

Option 4)

15

Incorrect

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