If the sum of $n$ terms of a AP is $nA + n^{2}B,$ where $A$ and $B$ are constants, then its common difference will be

Question

Dr. Abubacker · Accepted Answer

(d)
Given that, $S_{n} = nA + n^{2}B$
Putting $n = 1,\ 2,\ 3,\ldots,$ we get
$S_{1} = A + B,\ S_{2} = 2\ A + 4B,\ S_{3} = 3A + 9B$
………..,
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 $(A + B),\ (A + 3B),\ (A + 5B),\ldots$
$	herefore\ \$Common difference, $d = A + 3B - (A + B) = 2B$

Q. If the sum of $n$ terms of a AP is $nA + n^{2}B,$ where $A$ and $B$ are constants, then its common difference will be

Explanation

Reviewed by Dr. Abubacker

Want more practice?