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

Correct answer: (C) 0 < x < 10. x/(1-r)=5 ⇒ r=1-x/5 Since, G.P. contains infinite terms ∴-1 < r < 1 ⇒-1 < 1-x/5 < 1 ⇒ 0 < x < 10, x ≠ 5

Q42 / 110 · VITEEE 2023 · Mathematics

An infinite G.P. has first term ' \(x\) ' and sum ' 5 ', then \(\mathrm{x}\) belongs to

A
\(\mathrm{x} < -10\)
B
\(-10 < \) x \( < 0\)
Correct answer
C
\(0 < x < 10\)
D
None of these

Solution

\(\frac{\mathrm{x}}{1-\mathrm{r}}=5 \Rightarrow \mathrm{r}=1-\frac{\mathrm{x}}{5}\) Since, G.P. contains infinite terms \(\begin{aligned} & \therefore-1 < \mathrm{r} < 1 \\ & \Rightarrow-1 < 1-\frac{\mathrm{x}}{5} < 1 \Rightarrow 0 < \mathrm{x} < 10, \mathrm{x} \neq 5 \end{aligned}\)

Hence, the correct answer is option: 'C'.

An infinite G.P. has first term ' \(x\) ' and sum ' 5 ', then \(\mathrm{x}\) belongs to

Solution

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