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!