Question

If $a_1,a_2,a_3$, ____ $a_n$ are in A.P. and $a_1+a_4+a_7+\cdots +a_{16}=114$, then $a_1+a_6+a_{11}+a_{16}$ is equal to

Answer 1

Answer: 76

$a_1+a_4+a_7+\cdots +a_{16}=114$
$\Rightarrow 3(a_1+a_{16})=114$
$\Rightarrow a_1+a_{16}=38$
Now, $a_1+a_6+a_{11}+a_{16}=2(a_1+a_{16})=2\times 38=76$