Sequences And Series

Let \(l_{1}, l_{2}, \ldots, l_{100}\) be consecutive terms of an arithmetic progression with common difference \(d_{1}\), and let \(w_{1}, w_{2}, \ldots, w_{100}\) be consecutive terms of another arithmetic progression with common difference \(d_{2}\), where \(d_{1} d_{2}=10\). For each \(i=1,2, \ldots, 100\), let $R_{i}$ be a rectangle with length \(l_{i}\), width \(w_{i}\) and area $A_{i}$. If \(A_{51}-A_{50}=1000\), then the value of \(A_{100}-A_{90}\) is __________.