Question

The sum of an infinite $G.P.$ whose first term is $28$ and fourth term is $\frac{4}{49}$ is:

• A. $\frac{49}{5}$
• B. $\frac{98}{3}$
• C. $\frac{48}{7}$
• D. $\frac{18}{7}$

Answer 1

The correct option is B $\frac{98}{3}$

$a_1=28a_4=\frac{4}{49}$

$a_4=a{r}^3$

$28r^3=\frac{4}{49}$

$r^3=\frac{1}{49}\times \frac{1}{7}$

$\therefore r=\frac{1}{7}$

$\begin{array}{cc}\text{Sum of Infinite}G.P.=\frac{a}{1-r}& \\ =\frac{28}{1-\frac{1}{7}}=\frac{28}{6}\times 7& \\ =\frac{14}{3}\times 7& \\ =& \frac{98}{3}\end{array}$