# Number sequences

A number sequence is a series of numbers that are linked by a rule. If you know the rule, you can work out the next numbers in the sequence.

For example this is a number sequence

1,2,3,4,5,...

The terms of the above sequence are denoted by a and the index indicates the order number for that term. The first term is 2, the second term 4 and the third term 6. The general term is denoted by index n, which is the term's order number. The number sequence seems to have a clear rule about how its terms are formed. The order of a term is multiplied by two, so any term of the above sequence is obtained. For example, the 100th and 120th terms of a sequence are

If the rule of the sequence is known, any term of the sequence can be worked out. The first three terms for the sequence below are

### Recursive sequences

A recursive sequence is a sequence where each term is defined by using preceding terms.

Usually, we know the first terms and use them to work out the other terms in the sequence. The most well known recursive sequence is called the Fibonacci sequence.

# 0,1,1,2,3,5,8,13,21,34,55,...

Each term is the sum of two preceding ones

The ratio of two consecutive Fibonacci numbers tends to the golden ratio as *n* increases.

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