Question

An infinite GP has first term `x` and sum 5, then `x` belongs to (2004, 1M) `x<-10` (b) `-10<x<0` `0<x<10` (d) `x > 10`
A. `x lt -10`
B. `- 10 lt x lt 0`
C. `0 lt x lt 10`
D. `x gt 10`

Answer 1

Correct Answer - 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`