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!

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