In maths, a sequence is an ordered set of numbers. For example .
For this sequence, the rule is add four.
Each number in a sequence is called a term and is identified by its position within the sequence. We write them as follows.
The above sequence can be generated in two ways.
You can use a formula for the nth term. Here it would be . Adding the same amount (in this case ) generates each term. Each term will therefore be a multiple of .
However, the first term when is .
When , and so on.
The other way of generating this sequence is by using a recurrence relation, where each term is generated from the previous value.
When , .
When , .
The recurrence relation would therefore be . The starting value , would have to be provided. Note that the starting value can also be .
A sequence is defined by the recurrence relation and has .
a) Find the first five terms of the sequence.
b) Determine the formula for .
Therefore the sequence is
b) Note that we have powers of 3.
term 3 etc.