Let be consecutive terms of and arithmetic progression with common difference , and let , be consecutive terms of another arithmetic progression with common difference , where . For each , let be a re...

$ A_51-A_50 = (l_1+50 d_1)(w_1+50 d_2) - (l_1+49 d_1)(w_1+49 d_2) \\$ $= l_1 d_2 + w_1 d_1 + (50^2-49^2)d_1 d_2 \\ = 1000 \\$...

Let l_{1},l_{2},,l_{100} be consecutive terms of an arithmetic progression with common difference d_{1}, and let w_{1},w_{2}, ,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,,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 .: Sequence & Series (Mathematics)

Let

l_{1},l_{2},\ldots,l_{100}

be consecutive terms of and 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}

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