Determine the sum of all three-digit numbers which are

Solution

ATQ, Since, the sum of digits of the number is divisible by '3', the number must be divisible by '3' too. LCM (8 and 3) = 24 So, we need to find the sum of all three-digit numbers which are divisible by '24'. So, first three digit multiple of 24 = 120 And, last three-digit number that is divisible by 24 = 984 General term of an arithmetic progression = a + (n - 1) × d {Where 'a' is the first term, 'n' is the number of terms and 'd' is the common difference}. 984 = 120 + (n - 1) × 24 Or, 864 = 24n - 24 Or, 888 = 24n So, n = 37 So, required sum = (37/2) × (120 + 984) = 20,424