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Math and Logic

Rearrange the Dots

In the pattern below, we add a new row to the bottom of the triangle with every step. The next term will then be 10+5=15,10+5=15, and we can find the one after that by adding six: 15+6=2115+6=21.

We could extend this pattern as far as we want, making larger and larger triangles, but is it possible to skip straight to the number of dots in the 100th100^\text{th} triangle without calculating all the figures in between?

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