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 , 0 ) $
• C. $(0 , 10)$
• D. $[10 , \infty)$

Answer 1

Answer: (C)

If b is the first term and r is the common ratio of an infinite G.P. then sum is 5
$5=\frac{b}{1-r}$]
$1-r=\frac{b}{5}$
$r=1-\frac{b}{5}$
$r=\frac{5-b}{5}$
∴ -1 < r < 1
$\therefore -1<\frac{5-b}{5}<1$
- 5 < 5 - b < 5
- 5 < 5 - b < 5
- 10 < - b < 0
0 < b < 10
b $\in$ (0,10)