Question

STATEMENT - $1$ : The sum of first $11$ terms of the A.P: $2,6,10,14,\dots$ is $242.$
STATEMENT - $2$ : The sum of first $n$ terms of the A.P. is given by $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

• A. Statement - $1$ is True, Statement - $2$ is True, Statement - $2$ is a correct explanation for Statement - $1$
• B. Statement - $1$ is True, Statement - $2$ is True : Statement $2$ is NOT a correct explanation for Statement - $1$
• C. Statement - $1$ is True, Statement - $2$ is False
• D. Statement - $1$ is False, Statement - $2$ is True

Answer 1

The correct option is A Statement - $1$ is True, Statement - $2$ is True, Statement - $2$ is a correct explanation for Statement - $1$

Checking Statement $1$:

Given series: $2,6,10,14,\dots$

$n=11$

$a=2$

$d=6-2=4$

$\therefore S_{11}=\frac{11}{2}[2.2+(11-1\left)4\right]=242$

$\therefore$ Statement $1$ is True

$\therefore$ Statement $2$ is also True (general formula)

Statement $2$ is used to prove Statement $1$

Hence, statement $2$ is correct explanation for statement $1.$