Let \(\{{X_{nk},1\leq{k}\leq m_{n},n\geq1}\}\) be independent random variables with the Pareto distribution. Let \({X_{n(k)}}\) be the \(k^{th}\) largest order statistic from the \(n^{th}\) row of the array. Let, for \(j<i, R_{nij}=X_{n(j)}/X_{n(i)}\). The main aim of this paper is to present limit theorems involving weighted sums from the sequence \(\{R_{nij},\;n\geq1\}\). Thus, one can say that the author presents ”unusual” strong and weak laws of large numbers.