Sequence And Series Question 124
Question: The solution of the equation $ 1+a+a^{2}+a^{3}+…….+a^{x} $ $ =(1+a)(1+a^{2})(1+a^{4}) $ is given by $ x $ is equal to
Options:
A) 3
B) 5
C) 7
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ 1+a+a^{2}+…….+a^{x}=(1+a)(1+a^{2})(1+a^{4}) $
$ \Rightarrow $ $ \frac{(1-{a^{x+1}})}{(1-a)}=(1+a)(1+a^{2})+(1+a^{4}) $
$ \Rightarrow $ $ (1-{a^{x+1}})=(1-a)(1+a)(1+a^{2})(1+a^{4}) $
$ \Rightarrow $ $ (1-{a^{x+1}})=(1-a^{8}) $
$ \Rightarrow $ $ x+1=8 $
$ \Rightarrow $ $ x=7 $ .
BETA
