Sequence And Series Question 602
Question: If the $ 10^{th} $ term of a geometric progression is 9 and $ 4^{th} $ term is 4, then its $ 7^{th} $ term is
[MP PET 1996]
Options:
A) 6
B) 36
C) $ \frac{4}{9} $
D) $ \frac{9}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
Accordingly, $ ar^{9}=9 $ and $ ar^{3}=4 $
$ \Rightarrow $ $ r^{3}=\frac{3}{2} $ and $ a=\frac{8}{3} $ .
$ \therefore $ $ 7^{th} $ term $ i.e. $ $ ar^{6}=\frac{8}{3}{{( \frac{3}{2} )}^{2}}=6 $ . Trick: $ 7^{th} $ term is equidistant from $ 10^{th} $ and $ 4^{th} $ so it will be $ \sqrt{9\times 4}=6 $ .
BETA
