Sequence And Series Question 489
Question: If $ S_{n} $ denotes the sum of $ n $ terms of an arithmetic progression, then the value of $ (S_{2n}-S_{n}) $ is equal to
Options:
A) $ 2S_{n} $
B) $ S_{3n} $
C) $ \frac{1}{3}S_{3n} $
D) $ \frac{1}{2}S_{n} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ S_{2n}-S_{n}=\frac{2n}{2}{2a+(2n-1)d}-\frac{n}{2}{2a+(n-1)d} $ $ =\frac{n}{2}{4a+4nd-2d-2a-nd+d}=\frac{n}{2}{2a+(3n-1)d} $ $ =\frac{1}{3}.\frac{3n}{2}{2a+(3n-1)d}=\frac{1}{3}S_{3n} $ .
BETA
