Variance of a mean of three AR(1) values needs autocovariances, not autocorrelations

What will be the variance of $(X_1+X_2+X_3)/3$, if $X_1$, $X_2$ and $X_3$ are from an AR(1) series $X_t=\tfrac12X_{t-1}+Z_t$, where $Z_t\sim$ iid normal $(0,1)$?