Question

If $b$ is the first term of an infinite $G.P.$ whose sum is five, then $b$ lies in the interval.

• A. $(-\infty ,-10]$
• B. $(10,\infty )$
• C. $(0,10)$
• D. $(-10,0)$

Answer 1

The correct option is C $(0,10)$

first term $=b$

common ratio $=r$

$-1<r<1$ for infinte series

For infinite series ;

$S=\frac{b}{1-r}=5$

$\to b=5(1-r)$

Since $|r|<1$ for an infinite geometric series to converge, we have $-1<r<1\Rightarrow 0<1-r<2\Rightarrow 0<b<10$.

So option C is the correct answer.

interval of $b\in (0,10)$