Sequence And Series Question 128
Question: If the first term of a G.P. $ a_1,\ a_2,\ a_3,………. $ is unity such that $ 4a_2+5a_3 $ is least, then the common ratio of G.P. is
Options:
A) $ -\frac{2}{5} $
B) $ -\frac{3}{5} $
C) $ \frac{2}{5} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ a_1=1,\ a_2=r,\ a_3=r^{2},……. $
$ \therefore $ $ 4a_2+5a_3=4r+5r^{2} $ To be its minimum $ \frac{d}{dr}(4r+5r^{2})=0 $
$ \Rightarrow $ $ r=\frac{-2}{5} $ .
BETA
