Let $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots, \mathrm{a}_{11}$ be real numbers satisfying $\mathrm{a}_1=15,27-2 \mathrm{a}_2>0$ and $\mathrm{a}_{\mathrm{k}}=2 \mathrm{a}_{\mathrm{k}-1}-\mathrm{a}_{\mathrm{k}-2}$ for $\mathrm{k}=3,4, \ldots$, 11. If $\frac{a_1^2+a_2^2+\ldots+a_{11}^2}{11}=90$, then the value of $\frac{a_1+a_2+\ldots+a_{11}}{11}$ is equal to