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  4. If a1, a2, a3, an are in A.P. and a1+a4+a7+ dots +a16=114, then a1+a6+a11+a16 is equal to

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Q. If $a_{1}, a_{2}, a_{3}$, ____ $a_{n}$ are in A.P. and $a_{1}+a_{4}+a_{7}+ \dots +a_{16}=114$, then $a_{1}+a_{6}+a_{11}+a_{16}$ is equal to

Sequences and Series

Solution:

$a_{1}+a_{4}+a_{7}+\dots+a_{16}=114$
$\Rightarrow 3(a_{1}+a_{16})=114$
$\Rightarrow a_{1} + a_{16} = 38$
Now, $a_{1}+a_{6}+a_{11}+a_{16}=2(a_{1}+a_{16})=2\times 38 =76$