Question

The first term of an infinite geometric progression is xand its sum is 5. Then

• A. $0 \leq x \leq 10$
• B. $0 < x < 10$
• C. $- 10 < x < 0$
• D. $x > 10$

Answer 1

Answer: (B)

$0 < x < 10$

Answer 2

According to the given conditions, $5 = \frac{x}{1 - r}$, r being the

common ratio ⇒ $r = 1 - \frac{x}{5}$

Now, |r|< 1 i.e. $- 1 < r < 1$

⇒ $- 1 < 1 - \frac{x}{5} < 1$

⇒ $- 2 < - \frac{x}{5} < 0$

⇒ $2 > \frac{x}{5} > 0$ i.e. $0 < \frac{x}{5} < 2$,

∴ $0 < x < 10$