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An infinite GP has first term x and sum ...

An infinite GP has first term `x` and sum 5, then `x` belongs to

A

`x lt -10`

B

`- 10 lt x lt 0`

C

`0 lt x lt 10`

D

`x gt 10`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that, the sum of infinite terms of GP is
`S_(oo) = {((alpha)/(1 -r)","|r| lt1),(oo"," |r| ge 1):}`
`:. S_(oo) = (x)/(1 -r) = 5 " " [|r| lt 1]`
or `1 - r = (x)/(5)`
`rArr r = (5 -x)/(5)` exists only when `|r| lt1`
i.e. `-1 lt (5 -x)/(5) lt 1`
or `10 lt - x lt 0`
`rArr 0 lt x lt 10`
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