A sequence is a list of numbers (or a pattern) that are related to each other by a rule. The next number or pattern in the list can be worked out from the previous number or pattern using this rule.
Each number in the list is called a term. The first number is the first term, the second number is the second term, and so on.
The rule that links the terms is called the term-to-term rule.
To work out the next term in a sequence, work out what the rule is.
After a term-to-term rule has been worked out, always compare it against another pair of terms to make sure that it is correct.
A term-to-term rule is given as multiply the last term by 2 and subtract 3.
What are the next two terms in the sequence, if the first term is 5?
| Second term: | (5) x 2 - 3 | = 7 |
| Third term: | (7) x 2 - 3 | = 11 |
Answer: 7, 11
A sequence is made up from a set of lines.
How many lines will there be in the 5th and 6th terms of the sequence?
The first term has 3 lines; the second term has 5 lines. The term-to-term rule is add two lines. Check the next pair of terms: this is also add two lines. Use a table to work out the answer.
| Term | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of Sticks | 3 | 5 | 7 | 9 | 11 | 13 |
Answer: 11, 13