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# What Is the Fibonacci Sequence and Why is it Famous? Learn what the Fibonacci sequence is, its relationship to population growth, and how it can make you the life of the party.

By
Jason Marshall, PhD
Episode #16

## The Fibonacci Sequence and Rabbits It’s not often someone suggests that knowing some math could make you the life of the party, but that’s exactly what I’m going to do. Yes, a properly timed delivery of a few fun facts about the famed Fibonacci sequence just might leave your friends clamoring for more—because it really is that cool. So, without further ado, let’s continue our exploration of sequences that we began a few articles ago by jumping right in and talking about Fibonacci’s famous sequence.

## Review of Mathematical Sequences

As we’ve discussed, sequences in math are fairly simple things—they’re just lists of numbers arranged in some particular order. The number of sequences that can be written is infinite since any random list of numbers will do. But some types of sequences are decidedly non-random—one of which being the geometric sequence. In such a sequence, each element is obtained from the previous one by multiplying it by the same fixed number. For example: 2, 4, 8, 16, 32, is a geometric sequence where each successive element is obtained by multiplying the previous one by 2.

## Exponential Population Growth

In the last article, I used this particular sequence to describe how populations might grow. Starting with a single pair of organisms that produce one additional pair of offspring each reproductive cycle, the number of organisms will grow as: 2, 4, 8, 16, 32, and so on. After a few more generations, this sequence predicts that the population will become very large, very quickly. But does this type of sequence actually describe nature?

Well, it depends. This type of growth—so-called geometric or exponential growth—can, in fact, occur in some situations. But even if geometric growth occurs for a while, it can’t last forever since the quickly multiplying organisms will eventually deplete their resources—be it food or available living space—at which point their numbers must stop growing exponentially. But is that the only problem with describing population growth as a geometric sequence?

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