Question

The first term of an infinite G.P. is $1$ and any term is equal to the sum of all the succeeding terms. Find the series.

• A. $1,2,4,8,......$
• B. $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},.....$
• C. $1,\frac{1}{4},\frac{1}{8},.....$
• D. $1,\frac{1}{2},\frac{1}{4},\frac{1}{8},.....$

Answer 1

Answer: (D)

$1,\frac{1}{2},\frac{1}{4},\frac{1}{8},.....$

Let the common ratio of the infinite G.P. be $r$

Thus, the G.P. is $1,r,r^2,r^3....$

Sum of a infinte G.P. $=\frac{a}{1-r}$

Given, any term is equal to the sum of all the succeeding terms

Thus, $1=\frac{r}{1-r}$

$=>1-r=r$

$=>2r=1$

$=>r=\frac{1}{2}$

Thus, the G.P. is $1,\frac{1}{2},\frac{1}{4},\frac{1}{8},.....$