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

Question

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval : (A) ( - ∞ , - 10]  (B) ( - 10 , 0 )  (C) (0 , 10) (D) [10 , ∞)

Tardigrade Admin · Accepted Answer

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

∴ - 1 < \frac{5 - b}{5} < 1

- 5 < 5 - b < 5
- 5 < 5 - b < 5
- 10 < - b < 0
0 < b < 10
b

\in

(0,10)

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

$(- \infty, - 10]$

$(- 10, 0)$

$(0, 10)$

$[10, \infty)$

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
$∴ - 1 < \frac{5 - b}{5} < 1$
- 5 < 5 - b < 5
- 5 < 5 - b < 5
- 10 < - b < 0
0 < b < 10
b $\in$ (0,10)

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

(−∞,−10]

(−10,0)