An infinite G.P. has first term ' x ' and sum '5', then x belongs to [2004]

Question

An infinite G.P. has first term $' x'$ and sum '5', then $x$ belongs to [2004]

Smart Achievers · Accepted Answer

(3)

$\frac{x}{1 - r} = 5 \Rightarrow r = 1 - \frac{x}{5}$

$Since G.P. contains infinite terms$

$∴$ $- 1 < r < 1$

$\Rightarrow - 1 < 1 - \frac{x}{5} < 1 \Rightarrow - 2 < - \frac{x}{5} < 0$

$\Rightarrow - 10 < x < 0 \Rightarrow 0 < \frac{x}{5} < 2$

$∴$ $0 < x < 10$

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