Mathematics

Mathematics

Problem

Let l1,l2,…,l100l_1, l_2, \dots, l_{100} be consecutive terms of an arithmetic progression with common difference d1d_1, and let w1,w2,…,w100w_1, w_2, \dots, w_{100} be consecutive terms of another arithmetic progression with common difference d2d_2, where d1d2=10d_1 d_2 = 10. For each i=1,2,…,100i = 1, 2, \dots, 100, let RiR_i be a rectangle with length lil_i, width wiw_i and area AiA_i. If A51−A50=1000A_{51} - A_{50} = 1000, then the value of A100−A90A_{100} - A_{90} is ________.

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