Math CentralQuandaries & Queries


Question from Allie, a student:

1 3 6 10 15....

i know the pattern is +2 +3 +4 +5 and so on...but i dont know how to write an equation to find the nth term. help!


That is one pattern, but there could be many. If you multiply each term by
2, you get

2, 6, 12, 20, 30, ...

which is

1x2, 2x3, 3x4, 4x5, 5x6, ...

Do you see how to use that to find an expression for the original sequence?



Try this first. Try drawing patterns of dots representing
these sums:




Then try to find a way to fit multiple copies of one of these together into a square or rectangle. That should suggest a pattern to you; try a few more cases and see if it works.

Good Hunting!


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