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Explain how to calculate 75 + 72 + 69 + 66 + ... + 21 + 18 + 15 + ... + (-24) + (-27) + (-30) without a calculator.

 Aug 28, 2022
 #1
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-3

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!

 Aug 28, 2022

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