The correlation matrix off the random variables $Y_1,Y_2,Y_3,Y_4$ is $$ \begin{pmatrix} 1 & \rho & \rho^2 & \rho^3\\ \rho & 1 & \rho & \rho^2\\ \rho^2 & \rho & 1 & \rho \\ \rho^3 & \rho^2 & \rho & 1\\ \end{pmatrix},0<\rho<1$$ Each random variable has variance $\sigma^2$. Find the variance of $\bar{Y}_4$.
The answer given is $\bar{Y}_4=(\frac14+\frac{3\rho}{8}+\frac{\rho^2}{4}+\frac{\rho^3}{8})$
I do not know how to get this solution. My intructor does not offer any explanation, and any terms that I try to look do not result in anything useful