The sum to infinite terms of the progression 6,4 \frac{4}{5},3 \frac{21}{25},. . .... is

AP ICET 2016 Paper

Question : 138 of 200

Marks: +1, -0

The sum to infinite terms of the progression

6,4\;\;{4}/{5},3\;\;{21}/{25},. . ....

Solution:

Given :

6,4{4/5},3{21/25}........∞

or,

6,24/5,96/25,....∞

It represents an infinite G.P

=6,r={({96}/{25})}/{({24}/{5})}={({24}/{5})}/{6}={4}/{5}

∴S\;∞={a}/{1-r}={6}/{1-{4}/{5}}=6×5=30

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