If $b$ is the first term of an infinite G. P whose sum is five, then $b$ lies in the interval.
If $b$ is the first term of an infinite G. P whose sum is five, then $b$ lies in the interval.
$(-\infty,-10)$
$(10, \infty)$
$(0,10)$
$(-10,0)$
Solution
First term $=b$ and common ratio $=\mathrm{r}$
For infinite series, Sum $=\frac{b}{1-r}=5$ $\Rightarrow b=5(1-\mathrm{r})$
So, interval of $b=(0,10)$ as, $-1 < \mathrm{r} < 1$ for infinite GP.