# SAT – number properties

Q: What is the sum of all of the integers from 1 to 100?

Explanation: Don’t add 1 + 2 + 3 + 4 + … all the way up to 100! While it will work, it is a giant waste of time. Look for a pattern of numbers to pair up:

1 + 99 = 100

2 + 98 = 100

3 + 97 = 100

49 + 51 = 100

That’s 49 one hundreds. 49×100 = 4900. Now, add the numbers we have not counted yet: 100 and 50.

4900 + 100 + 50 = 5050.

My TI-84 Plus program ‘SUMATOB’ will find this sum, too.

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