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  4. In increasing geometric series of positive terms, the difference between the fifth and fourth terms is 576 and the difference between the second and first term is 9. The sum of the first five terms of this series, is

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Q. In increasing geometric series of positive terms, the difference between the fifth and fourth terms is 576 and the difference between the second and first term is 9. The sum of the first five terms of this series, is

Sequences and Series

Solution:

$ ar ^4- ar ^3=576$
$a ( r -1)=9$
$\therefore ar ^3( r -1)=576$
$\Rightarrow r ^3=\frac{576}{9} \Rightarrow r ^3=64 $
$ r =4 \text { and } a =3$
$S _5=\frac{3\left(4^5-1\right)}{4-1}=1023$