# Adding Four Consecutive Numbers

Can you find a short cut to find the sum of four consecutive numbers, without adding all four together?

Will your method always work? Explain.

*Hint*: Consecutive numbers are 1, 2, 3, 4, ... 12, 13, 14, 15 ...

*Discussion:*

Add the first and the last numbers and double that answer.

Make a chart with five columns. Put four consecutive numbers one in each cell of a row and their sum in the fifth row. Repeat for several other numbers and see what kiind of pattern there is.

n + (n + 1) + (n + 2) + (n + 3)

[n + (n + 3)] * 2

The same. Proof positive for all numbers.

*Mind boggler*:

*Enjoy!*