Find the number of negative integers greater than -500 that are divisible by 33.

Also find their sum.
How do I set up this problem?

let a = -33 , (the last one)

let d = -33 , going backwards

a+(n-1)d = appr -500
-33 + (n-1)(-33) = -500

-33 -33n + 33 = -500
-33n = -500
n = 15.15..
So there are 15 terms, and term(15) = -33 + 14(-33) = -495

so we have -495 , -462, -429, ... -66, -33

sum(15) = (15/2)(first + last) = (15/2)(-495-33) = -3960

To find the number of negative integers greater than -500 that are divisible by 33, we need to determine the range of numbers and then identify the multiples of 33 within that range. Here's how to set up the problem step by step:

1. Determine the possible range of numbers: We are looking for negative integers greater than -500. So, the range of numbers we need to consider is from -500 to -1 (excluding 0 since it is neither positive nor negative).

2. Identify the multiples of 33 within the range: To determine the multiples of 33, divide each number in the range by 33 and check if the remainder is zero.

3. Count the number of multiples: Count the total number of negative integers within the range that are divisible by 33. Each multiple will add to this count.

4. Calculate their sum: Add up all the negative integers greater than -500 that are divisible by 33 to find their sum.

By following these steps, we can determine both the number of negative integers greater than -500 that are divisible by 33 and their sum.