Sequence And Series Question 95
Question: If $ a_1,a_2,a_3….a_{n} $ are in H.P. and $ f(k)=( \sum\limits_{r=1}^{n}{a_{r}} )-a_{k} $ then $ \frac{a_1}{f(1)},\frac{a_2}{f(2)},\frac{a_3}{f(3)},…\frac{a_{n}}{f(n)} $ are in
Options:
A) A.P
B) G.P
C) H.P
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(k)+a_{k}=\sum\limits_{r=1}^{n}{a_{r}}=\lambda ,(say) $
$ \therefore f(k)=\lambda -a_{k} $
$ \Rightarrow \frac{{f_{(k)}}}{a_{k}}=\frac{\lambda }{a_{k}}-1 $
$ \therefore \frac{f(1)}{a_1},\frac{f(2)}{a_2},…,\frac{f(n)}{a_{n}} $ are in A.P. So $ \frac{a_1}{f(1)},\frac{a_2}{f(2)},…\frac{a_{n}}{f(n)} $ are in H.P.
BETA
