Question

Let $x_1,x_2,.....x_n$ be in an AP of $x_1+x_4+x_9+x_{11}+x_{20}+x_{22}+x_{27}+x_{30}=272$, then $x_1+x_2+x_3+.....+x_{30}$ is equal to

• A. $1020$
• B. $1200$
• C. $716$
• D. $2720$

Answer 1

The correct option is A $1020$

If an AP consist of $30$ terms, Then $x_1+x_{30}=x_4+x_{27}=x_9+x_{22}=x_{11}+x_{20}$
$\because x_1+x_4+x_9+x_{11}+x_{20}+x_{27}+x_{30}=272$
$\Rightarrow (x_1+x_{30})+(x_4+x_{27})+(x_9+x_{22})+(x_{11}+x_{26})=272$
$\Rightarrow 4(x_1+x_{30})=272$
$\Rightarrow x_1+x_{30}=\frac{272}{4}=68$
$S_{30}=\frac{30}{2}(x_1+x_{30})=15\times 68=1020$