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.
  1. $(-\infty,-10)$
  2. $(10, \infty)$
  3. $(0,10)$
  4. $(-10,0)$

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.

Asked in: JEE Main 2018 (15 Apr Shift 1 Online)

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