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 , 3 . . . . . . . . . . 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 __

Step-by-step solution

Given l 1 , l 2 . . . l 100 are consecutive terms of an A . P Now let T 1 = a and common difference = d 1 And similarly for A . P w 1 , w 2 , . . . w 100 , T 1 = b and common difference = d 2 Now given, A 51 - A 50 = l 51 w 51 - l 50 w 50 ⇒ a + 50 d 1 b + 50 d 2 - a + 49 d 1 b + 49 d 2 = 1000 ⇒ 50 b d 1 + 50 a d 2 + 2500 d 1 d 2 - 49 a d 2 - 49 b d 1 - 2401 d 1 d 2 = 1000 ⇒ b d 1 + a d 2 + 99 d 1 d 2 = 1000 So, b d 1 + a d 2 = 10 as given  d 1 d 2 = 10 Now finding A 100 - A 90 = l 100 w