Sequence And Series Question 512
Question: The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be
[MNR 1979; RPET 1992, 95]
Options:
A) 6
B) 3
C) 4
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ ar=2 $ and $ {S_{\infty }}=8=\frac{a}{1-r} $
$ \Rightarrow $ $ 8=\frac{2}{r(1-r)}( \because \ a=\frac{2}{r} ) $
$ \Rightarrow $ $ 4r(1-r)=1\Rightarrow 4r-4r^{2}-1=0 $
$ \Rightarrow $ $ 4r^{2}-4r+1=0\Rightarrow ( r-\frac{1}{2} )(4r-2)=0\Rightarrow r=\frac{1}{2} $ So first term $ a=4 $ .
BETA
