Basic, GCSE(F),

A **sequence** is a list of numbers, or a pattern. The numbers, or patterns, 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 the 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, it is often necessary to work out what the rule is. Compare two terms, and determine how the second rule has changed from the first.

Check: 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.

1. 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?

Answer: 7, 11

The second term is given by 5 x 2 - 3 = 7

The third term is 7 x 2 - 3 = 11.

2. 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?

Answer: 11, 13

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 |

Our iOS app has over 1,000 questions to help you practice this and many other topics.

Available to download free on the App Store.

Available to download free on the App Store.