Sequence And Series Question 493
Question: If $ S_{k} $ denotes the sum of first $ k $ terms of an arithmetic progression whose first term and common difference are $ a $ and $ d $ respectively, then $ S_{kn}/S_{n} $ be independent of $ n $ if
Options:
A) $ 2a-d=0 $
B) $ a-d=0 $
C) $ a-2d=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{S_{kn}}{S_{n}}=\frac{(kn/2){2a+(kn-1)d}}{(n/2){2a+(n-1)d}}=k{ \frac{(2a-d)+knd}{(2a-d)+nd} } $ $ i.e. $ if $ 2a-d=0 $ , then this becomes $ \frac{k^{2}nd}{nd}=k^{2} $ which is obviously independent of $ n $ .
BETA
