Find the next term: 1, 2, 4, 8, 16. Harder than you think?

Geometry Level 3

A circle has been cut by n-1 lines. Let S be the sequence of the maximum number of sections inside the circle created. (The nth term refers to the number of sections created by n-1 lines.) Here are the first few terms of the sequence S: 1, 2, 4, 8, 16 What is the next term of the sequence S?

See more problems on sequences in geometry.

Inspired by 3Blue1Brown video . Image Credit: Archimedes Lab , Authors: G. Sarcone, M.-J. Waeber

A different solution 31 33 32

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1 solution

1 2
Jul 11, 2018
  • The general term for the sequence is 1 + nC2 + nC4
  • Therefore 1+15+15=31

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