In an infinite G P , every term is equal to the sum of all terms that follow it - Maths - Sequences and Series

Question

​In an infinite G P , every term is equal to the sum of all
terms that follow it Find r

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Let the first term be a and common ratio be r 
Sum of infinite terms=a1-rSum of all terms that follow first term=a1-r-aAs it will be equal to first term 
So ,a=a1-r-a2a=a1-r2=11-r2-2r=12r=1r=12   ANS
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​In an infinite G.P., every term is equal to the sum of all terms that follow it. Find r

In an infinite G.P., every term is equal to the sum of all terms that follow it. Find r