Sequence And Series Question 522
Question: If $ \frac{{a^{n+1}}+{b^{n+1}}}{a^{n}+b^{n}} $ be the A.M. of $ a $ and $ b $ , then $ n= $
[MP PET 1995]
Options:
A) 1
B) $ -1 $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{{a^{n+1}}+{b^{n+1}}}{a^{n}+b^{n}}=\frac{a+b}{2} $
$ \Rightarrow $ $ {a^{n+1}}-ab^{n}+{b^{n+1}}-ba^{n}=0 $
$ \Rightarrow $ $ (a-b)(a^{n}-b^{n})=0 $ If $ a^{n}-b^{n}=0 $ . Then $ {{( \frac{a}{b} )}^{n}}=1={{( \frac{a}{b} )}^{0}} $ . Hence $ n=0 $ .
BETA
