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

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

1. A

$\left(-\mathrm{\infty },-101$)

2. B

$\left(-10,0\right)$

3. C

$\left(0,10\right)$

4. D

$\left[10,\mathrm{\infty }\right)$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Let $b,br,b{r}^{2},\dots \dots$ been infinite G.P. with first term, common ratio and sum = 5.

$\therefore 5=\frac{b}{1-r};|r|<1⇒\frac{b}{5}=1-r⇒r=1-\frac{b}{5}$

Now, $|r|<1⇒\left|1-\frac{b}{5}\right|<1⇒-1<1-\frac{b}{5}<1$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)