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!

 

 

Dr. Robert Sweetland's notes
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