## Sequence This

By Ariel Marcy, 24 May 2023

**Difficulty: Tricky**

Consider the following sequence of numbers. What number comes next?

1, 1, 2, 3, 5, 8, 13…

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

Find the difference between each of the numbers in the sequence. For example, the difference between 1 and 1 is 0, and between 1 and 2 is 1. If you continue this, what pattern do you notice?

## Brainteaser answer

The next number is 21.

This is the famous Fibonacci sequence, which is found frequently in nature and has applications in art, maths, design, and architecture. The sequence is created by adding the two previous numbers together, starting with 1+1, which equals 2.

When you continue this, it becomes 1+2 = 3, and then 3+2= 5, and so on.

As a result, the difference between the numbers is also a Fibonacci sequence (0, 1, 1, 2, 3, 5). Here, 8 must be the next number in the sequence so adding 8 to 13 gives us 21:

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