Question

the first term of an infinite gp is 1 and every term is equals to the sum of the sucessive terms then its fourth term will be-

Answer 1

As per the condition Sum of all terms following first term i.e. r+ r²+ r³+............ =1(First term)  

→{r/(1−r)} =1  

→ r=1−r  

and 2r=2 i.e r= 1/2  

Hence the series is 1, 1/2, 1/4, 1/8, 1/16...............

therefore  the fourth term is 1/8.