Question

If the sum of an infinite G.P, whose first term is 9, is x, then x belongs to

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

In an infinite G.P. , for the sum to be finite, the common ratio r should lie between -1 and 1.

Or -1 < r < 1

$\frac{9}{1-r}$ = x [ Sum of the G.P.]

$\Rightarrow$ x = $\frac{9}{1-r}$

$\Rightarrow$ r = $\frac{x-9}{x}$

-1 < r < 1

$\Rightarrow$ -1 < $\frac{x-9}{x}$ < 1

We will split the inequality as

$\frac{x-9}{x}$ > - 1 and $\frac{x-9}{x}$ < 1

x - 9 > - x and x - 9 < x

2x > 9 and -9 < 0

$\Rightarrow$ x > $\frac{9}{2}$ and -9 is less than zero for all values of x. So we don't have to use this part, because it does not impose any

condition.