Sequence And Series Question 622
Question: Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is
[AIEEE 2002]
Options:
A) 5
B) 3/5
C) 8/5
D) 1/5
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{a}{1-r}=20 $ …..(i) $ \frac{a^{2}}{1-r^{2}}=100 $ ?..(ii) From (i) and (ii), $ \frac{a}{1+r}=5 $ , $ [ \because a=20(1-r)by(i) ] $
Þ $ \frac{20(1-r)}{1+r}=5 $
$ \Rightarrow 5r=3 $
Þ $ r=3/5 $ .
BETA
