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]

• A. A - B
• B. A + B
• C. 2A
• D. 2B

Answer 1

Given that $S_n=nA+n^{2}B$
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.