math

A simple fractal tree Grows in stages. A each new stage, two new line segments branch out from each segment at the top of the tree. The first five stages are shown. How many line segments need to be drawn to create stage 20?

Stage 1- 1
Stage 2 - 3
Stage 3 - 7
Stage 4 -15
Stage 5 - 31 branches

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  1. Does the sequence look anything like powers of 2?

    2 4 8 16 32 ...

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  2. (2^n) - 1

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