In this paper, we discuss a certain nonautonomous Beverton-Holt equation of higher order. After a brief introduction to the classical Beverton-Holt equation and recent results, we solve the higher-order Beverton-Holt equation by rewriting the recurrence relation as a difference system of order one. In this process, we examine the existence and uniqueness of a periodic solution and its global attractivity. We continue our analysis by studying the corresponding second Cushing-Henson conjecture, i.e., by relating the average of the unique periodic solution to the average of the carrying capacity.