If a1, a2, a3, …., an are in A.P. and

$a_{1}+a_{4}+a_{7}+a_{10}+a_{13}+a_{16}=114$

$\Rightarrow \frac{6}{2}\left(a_{1}+a_{16}\right)=114$

$\Rightarrow a_{1}+a_{16}=38$

So, $\mathrm{a}_{1}+\mathrm{a}_{6}+\mathrm{a}_{11}+\mathrm{a}_{16}=\frac{4}{2}\left(\mathrm{a}_{1}+\mathrm{a}_{16}\right)$

$=2 \times 38=76$