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 5^{th} and 6^{th} 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

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