Sequence And Series Question 361
Question: A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then the common ratio is
Options:
A) 5
B) 1
C) 4
D) 3
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Let the G.P be $ a,ar,ar^{2},…… $ $ S=a+ar+ar^{2}+…….+to2ntern=\frac{a(r^{2n}-1)}{r-1} $ The series formed by taking term occupying odd places is $ S_1=a+ar^{2}+ar^{4}+…….. $ to n terms $ S_1=\frac{a[ {{(r^{2})}^{n}}-1 ]}{r^{2}-1}\Rightarrow S_1=\frac{a(r^{2n}-1)}{r^{2}-1} $ Now, $ S=5S_1 $ or $ \frac{a(r^{2n}-1)}{r-1}=5\frac{a(r^{2n}-1)}{r^{2}-1} $
$ \Rightarrow 1=\frac{5}{r+1}\Rightarrow r+1=5\therefore r=4 $
BETA
