Sequence And Series Question 419
Question: A series is such that its every even term is ‘a’ times the term before it and every odd term is c times the term before it. The sum of 2n term of the series is (the first term is unity)
Options:
A) $ \frac{(1-c^{n})(1-a^{n})}{1-ac} $
B) $ \frac{(1+a)(1-c^{n}a^{n})}{1-ac} $
C) $ \frac{(1+c^{n})(1+a^{n})}{1-ac} $
D) $ \frac{(1+a)(1+c^{n}a^{n})}{1+ac} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Clearly the required series is $ 1+a+ca+a(ca)+c(aca)+a(caca)+…….. $ ….to 2n terms $ =1+a+ca+ca^{2}+c^{2}a^{2}+c^{2}a{{+}^{3}} $ …..to 2n terms =( $ 1+ca+c^{2}a^{2}+ $ ?…. to n terms) + $ (a+ca+c^{2}a^{3}+…….tonterms) $ $ =\frac{1{1-{{(ca)}^{n}}}}{1-ca}+\frac{a{1-{{(ca)}^{n}}}}{1-ca} $ $ =\frac{(1+a)(1-c^{n}a^{n})}{1-ca} $
BETA
