Systematic sampling is efficient precisely when the population carries a linear trend

Let $V^2_{SY}$ be the variance of the usual estimator in a systematic sampling design and $V^2_{SRS}$ the variance of the sample mean in a SRSWOR design. It is known that the population has a linear trend, i.e., $y_i$ is approximately equal to $ic$, for a positive $c$, $i=1,2,\dots,N$. Then: