Understand Fibonacci Sequences

Fibonacci was an Italian mathematician from Pisa, who invented the following sequence in the year 1202:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...

After the first two terms, each term is formed by adding the two previous terms.

So here,

2 = 1 + 1

3 = 2 + 1

5 = 3 + 2

8 = 5 + 3

13 = 8 + 5 etc...

Fibonacci used 1 and 1 as his starting numbers, but any two numbers can be used.

Example

Work out the missing term in this Fibonacci sequence:

2, 2, 4, ?, 10, 16 ...

Answer

Look at the first two terms, which add to give 4, the third term.

The missing term is therefore 2 + 4 = 6

Check that the next term works too

4 + 6 = 10

6 + 10 = 16

Let's have a go at some questions now.