Sequence And Series Question 217
Question: The first term of an infinite geometric progression is $ x $ and its sum is 5. Then
[IIT Screening 2004]
Options:
A) $ 0\le x\le 10 $
B) $ 0<x<10 $
C) $ -10<x<0 $
D) $ x>10 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 5=\frac{x}{1-r} $
$ \Rightarrow $ $ 5-5r=x $
$ \Rightarrow $ $ r=1-\frac{x}{5} $ As $ |r|,<,1 $ i.e., $ | ,1-\frac{x}{5}, |<1 $ $ -1<1-\frac{x}{5}<1 $ $ -5<5-x<5=-10<-x<0=10>x>0 $ i.e, $ 0<x<10 $ .
BETA
