Explain how to calculate 75 + 72 + 69 + 66 + ... + 21 + 18 + 15 + ... + (-24) + (-27) + (-30) without a calculator.
+30 We can immediately cancel out all numbers between 30 - 0 inclusive.
So that leaves us with 75 + 72 + 69 + 66... + 36 + 33
The remaining is simple. We realize that 33 + 75 = 108 and 36 + 72 = 108. This pattern continues.
There are 14 numbers bewteen 75 and 33, so we have 7 groups of 108.
7 x 108 = 756
756
Hope this helps!
