Adding consecutive numbers between two
numbers
Choose two 2-digit numbers less than 20
(no limits for experts).
Add all the numbers between them:
Add the numbers;
Subtract the numbers and add 1;
Multiply half the sum by this difference + 1, OR
Multiply the sum by half the difference + 1.
Example:
If the two numbers selected are 6 and 19:
Add the numbers: 6 + 19 = 25.
Subtract the numbers: 19 - 6 = 13. Add 1: 13 + 1 = 14.
Multiply 25 by half of 14: 25 × 7 = 175.
So the sum of the numbers from 6 through 19 is 175.
See the pattern?
If the two numbers selected are 4 and 18:
Add the numbers: 4 + 18 = 22.
Subtract the numbers: 18 - 4 = 14. Add 1: 14 + 1 = 15.
Multiply half of 22 by 15: 11 × 15 = 165 (10 × 15 + 15).
So the sum of the numbers from 4 through 18 is 165.
Practice with examples restricted to less than 20, then advance to larger numbers. You will impress your friends when you beat the calculator.