Sequence And Series Question 91
Question: If $ S_{n} $ denotes the sum of first n terms of an A.P. whose first term is a and $ S_{nx}/S_{x} $ is independent of x, then $ S_{p}= $
Options:
A) $ p^{3} $
B) $ p^{2}a $
C) $ pa^{2} $
D) $ a^{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \frac{S_{nx}}{S_{x}}=\frac{\frac{nx}{2}[2a+(nx-1)d]}{\frac{x}{2}[2a+(x-1)d]}=\frac{n[(2a-d)+nxd]}{(2a-d)+xd} $ For $ \frac{S_{nx}}{S_{x}} $ to be independent of x, 2a-d=0 or 2a=d Now, $ S_{p}=\frac{p}{2}[2a+(p-1)d]=p^{2}a $
BETA
