A problem by anweshan bor

Level pending

Find the sum of all the three digit numbers which leave the remainder 3 when divided by 5.


The answer is 99090.

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2 solutions

Tony Sprinkle
Jan 4, 2015

This describes the sum of the first 180 180 terms of the arithmetic sequence with first term a 1 = 103 a_1 = 103 and common difference d = 5 d = 5 . The sum is given by:

S 180 = 180 2 ( a 1 + a 180 ) = 90 ( 103 + 998 ) = 99090 S_{180} = \frac{180}{2}(a_1 + a_{180}) = 90(103 + 998) = \boxed{99 090}

Shiv Ram
Jan 4, 2015

According to the question, the series is 103,108,113.... 998 Find the n digits by (l-a/d)+1 Using sum of series formula n/2(2a+(n-1)d) we get the answer

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