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2, 5, 10, 17, 26... What comes next?

A preview of " Sequences" Join Brilliant Premium

In these quizzes, we'll start by focusing on two specific types of sequences: arithmetic sequences and geometric sequences. However, these are just two cases that will lay a foundation. There is as much variety in sequence types as you can imagine!

Consider: Conway’s ‘Look and Say’ Sequence
Each term is the result of speaking the previous term out loud. For example, 1211 is pronounced “one 1, one 2, two 1's,” making the next term 111221. \[1, 11, 21, 1211, 111221, 312211, 13112221, ...\]

How long do you think it takes for the first 4 to appear?

You might already be familiar with this one!

The Fibonacci Sequence
Each term is the sum of the two previous terms. \[0, 1, 1, 2, 3, 5, 8, 13,\ldots\]

How many of the first 900 Fibonacci numbers are even?

And here's one last example -- a sequence that's deeply connected with geometry:

The Hexagonal Numbers
The number of distinct dots in a pattern of the outlines of regular hexagons when the hexagons are overlaid so that they share one vertex. \[1, 6, 15, 28,...\]

This chapter will explore these three sequences and many more!

Master the problem solving skills of Algebra Through Puzzles.

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