What is the sum of all 3-digit numbers that give a remainder of 5 when they are divided by 50?

Explanation

The sequence is 105, 155, \dots, 955. This is an arithmetic progression with a=105, d=50, and l=955. The number of terms n = \frac{955-105}{50} + 1 = 18. Sum = \frac{18}{2} \times (105 + 955) = 9 \times 1060 = 9540.

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