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

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An infinite G.P. has first term ‘x’ and sum ‘5’, then x belongs to
1). 0 ≤ x ≤ 10
2). -10 < x < 0
3). 0 < x < 10
4). -10 ≤ x ≤ 0


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2 vote
Answered by on | Votes 2 |

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

Since G.P. contains infinite terms

∴ –1 < r < 1

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

⇒ -10 < - x < 0

⇒ 0 < x < 10

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