Question

Each of these questions contains two statements, Statement 1(Assertion) and Statement 2(Reason).

Statement-I : If sum of n terms of a series is $6n^2+3n+1$, then the series is in A.P.

Statement-II : Sum of n terms of an A.P. is always of the form $a{n}^2+bn$, where $a$ and $b$ are constant.

State which of the following is correct :

(A) Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
(B) Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I
(C) Statement-I is true, Statement-II is false
(D) Statement-I is false, Statement-II is true

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

Answer: (D)

$D$

We know sum of an A.P is $S_n=\frac{n}{2}(2a+(n-1\left)d\right)=(a-d)n+\frac{d}{2}{n}^2$, where $a$ & $d$ are the first term and common difference respectively.
Hence statement 2 is true and statement 1 is wrong.