Question

The first term of an infinite G.P. is 1 and every term is equals to the sum of the successive terms, then its fourth term will be

• A. $\frac{1}{2}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{1}{16}$

Answer 1

The correct option is B $\frac{1}{8}$

Let $1,r,r^2,r^3,....$ are in $G.P.$

As per the condition sum of all terms following first term.

$i.e.$ $r+r^2+r^3+...=1$ (First term )

$\Rightarrow$ $\frac{r}{1-r}=1$

$\Rightarrow$ $r=1-r$

$\Rightarrow$ $2r=1$

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

$\therefore$ The series is $1,\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16}....$

$\therefore$ The fourth term is $\frac{1}{8}.$