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

Question

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

Answer 1

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