Question

the first term of an infinite GP is 1 and every term is equal to the sum of the successive terms then its fourth term will be

Answer 1

We know that in a Geometric Progression, there's a common ratio that forms the series.

Let's assume the common ratio be r.

Acc,to ques, first term = 1.

Then the series will be 1, r, r^2, r^3.....

Acc. to ques r^2  = r + 1.

or we can form a quadratic equ: r^2 - r - 1 = 0.

With the help of Sridhar acharya formula you'll get the vaue of r = (1 +- (5)^-2)/2

Accordingly, the fourth term will be cube of r. i.e. ((1 +- (5)^-2)/2)^3 = 4.236 (Ans)

Answer 2

Answer:- 1, 1/2, 1/4, 1/8, 1/16

Fourth term-1/8 i.e. 0.125

(Can be obtained from the G.P.)

Step-by-step explanation:-

Let the GP be 1, r, r² , r³............

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...............