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## 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 $10+5=15,$ and we can find the one after that by adding six: $15+6=21$.

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 $100^\text{th}$ triangle without calculating all the figures in between?