Find the sum of all the numbers between and which is divisible by .
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The sequence of numbers forms an arithmetic progression with a common difference of d = 9 9 .
The number of terms is n = 9 9 2 0 0 0 0 = 2 0 2 . The last term is a 2 0 2 = 9 9 ( 2 0 2 ) = 1 9 9 9 8 . The first term is a 1 = 9 9 . So the terms are ( 9 9 , 1 9 8 , 2 9 7 . . . 1 9 9 9 8 ) .
By using the formula for the sum, we get
s = 2 n ( a 1 + a 2 0 2 ) = 2 2 0 2 ( 9 9 + 1 9 9 9 8 ) = 2 0 2 9 7 9 7