Sequence And Series Question 619
Question: If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are
[RPET 1999]
Options:
A) 3/2, 1/2
B) 1, 1/2
C) 3/2, 2
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{a}{1-r}=3 $ ?..(i) and $ \frac{a^{2}}{1-r^{2}}=3 $ …..(ii) From (i) and (ii), $ \frac{a}{1+r}=1\Rightarrow a=1+r $ From (i), $ \frac{1+r}{1-r}=3\Rightarrow r=\frac{1}{2} $ , from (i), a = 3/2 So, first term = 3/2 and common ratio = 1/2.
BETA
