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Sequences and Series question

2022 · Shift 1 · Q24
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  5. /2022 · Shift 1 · Q24

Sequences and Series question

2022 · Shift 1 · Q24

JEE AdvancedMathematicsSequences and SeriesNumerical+3 / −1
Let l1,l2,…,l100l_{1}, l_{2}, \ldots, l_{100}l1​,l2​,…,l100​ be consecutive terms of an arithmetic progression with common difference d1d_{1}d1​, and let w1,w2,…,w100w_{1}, w_{2}, \ldots, w_{100}w1​,w2​,…,w100​ be consecutive terms of another arithmetic progression with common difference d2d_{2}d2​, where d1d2=10d_{1} d_{2}=10d1​d2​=10. For each i=1,2,…,100i=1,2, \ldots, 100i=1,2,…,100, let RiR_{i}Ri​ be a rectangle with length lil_{i}li​, width wiw_{i}wi​ and area AiA_{i}Ai​. If A51−A50=1000A_{51}-A_{50}=1000A51​−A50​=1000, then the value of A100−A90A_{100}-A_{90}A100​−A90​ is ‾\underline{\hspace{2cm}}​.
Numerical answer
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