Question

If the sum of $n$ terms of an A.P. is $n A + n ^ { 2 } B$ , where $A , B$ are constants, then its common difference will be.

• A. $A - B$
• B. $A + B$
• C.
• D. $2 B$

Answer 1

Answer: (D)

$2 B$

Answer 2

Given that $S _ { n } = n A + n ^ { 2 } B$

Putting $n = 1,2,3 , \ldots \ldots \ldots \ldots$ we get

$S _ { 1 } = A + B , S _ { 2 } = 2 A + 4 B , S _ { 3 } = 3 A + 9 B$

Therefore $T _ { 1 } = S _ { 1 } = A + B , T _ { 2 } = S _ { 2 } - S _ { 1 } = A + 3 B$

$T _ { 3 } = S _ { 3 } - S _ { 2 } = A + 5 B$,

Hence the sequence is $( A + B ) , ( A + 3 B ) , ( A + 5 B ) , \ldots \ldots \ldots$

Here $a = A + B$ and common difference $d = 2 B$.