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what is the sum of all positive interger less than 5050 that are divisible by 33

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Full solution

Q. what is the sum of all positive interger less than 5050 that are divisible by 33
  1. Identify Smallest/Largest Divisible Integers: Identify the smallest and largest positive integers less than 5050 that are divisible by 33. The smallest positive integer divisible by 33 is 33, and the largest is 4848 because 4848 is the largest multiple of 33 that is less than 5050.
  2. Find Count of Divisible Integers: Find out how many integers there are that are divisible by 33 and less than 5050. To find the count, use the formula for the number of terms in an arithmetic sequence: n=(last term−first term)/common difference+1n = (\text{last term} - \text{first term}) / \text{common difference} + 1. Here, the last term is 4848, the first term is 33, and the common difference is 33 (since we're looking for multiples of 33). n=(48−3)/3+1=45/3+1=15+1=16n = (48 - 3) / 3 + 1 = 45 / 3 + 1 = 15 + 1 = 16.
  3. Calculate Sum of Arithmetic Sequence: Calculate the sum of the arithmetic sequence.\newlineThe sum SS of an arithmetic sequence can be found using the formula S=n2×(first term+last term)S = \frac{n}{2} \times (\text{first term} + \text{last term}).\newlineHere, n=16n = 16, the first term is 33, and the last term is 4848.\newlineS=162×(3+48)=8×51S = \frac{16}{2} \times (3 + 48) = 8 \times 51.
  4. Perform Multiplication for Sum: Perform the multiplication to find the sum.\newlineS=8×51=408S = 8 \times 51 = 408.

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