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

3-digit numbers that leave remainder 5 when divided by 50 are of the form 50k + 5. The smallest is 105 (k=2) and the largest is 955 (k=19). These form an AP: 105, 155, 205, ..., 955. Number of terms n = (955 − 105)/50 + 1 = 18. Sum = n/2 × (first + last) = 18/2 × (105 + 955) = 9 × 1060 = 9540.