Sequence And Series Question 645
Question: If the sum of $ n $ terms of an A.P. is $ nA+n^{2}B $ , where $ A,B $ are constants, then its common difference will be
[MNR 1977]
Options:
A) $ A-B $
B) $ A+B $
C) $ 2A $
D) $ 2B $
Show Answer
Answer:
Correct Answer: D
Solution:
Given that $ =\frac{n(n+1)}{2}[ \frac{n(n+1)}{2}+\frac{2n+1}{3} ] $ Putting $ n=1,\ 2,\ 3,\ …………., $ we get $ S_1=A+B,,S_2=2A+4B,S_3=3A+9B $ …………………………………………………….. …………………………………………………….. Therefore $ T_1=S_1=A+B,\ T_2=S_2-S_1=A+3B, $ $ T_3=S_3-S_2=A+5B $ , …………………………………………………….. …………………………………………………….. Hence the sequence is $ (A+B),(A+3B),\ (A+5B),…….. $ Here $ a=A+B $ and common difference $ d=2B $ .
BETA
