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Learn about and revise how to continue sequences and find the nth term of linear and quadratic sequences with GCSE Bitesize AQA Maths.
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Sequences. Number sequences are sets of numbers that follow a pattern or a rule. If the rule is to add or subtract a number each time, it is called an arithmetic sequence. If the rule is to ...
The 𝒏th term refers to a term's position in the sequence, for example, the first term has 𝒏 = 1, the second term has 𝒏 = 2 and so on.
A "series" is what you get when you add up all the terms of a sequence; the addition, and also the resulting value, are called the "sum" or the "summation". For instance, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the sum "1 + 2 + 3 + 4", and the value of the series is 10.
To refer to any term of a sequence, we use the un u n notation, where n n indicates the term we're referring to. For instance, if we're dealing with the sequence 3, 7, 11, 15, 19, 23, … 3, 7, 11, 15, 19, 23, … we would refer to the first, second and third terms as: u1 = 3 u 1 = 3. u2 = 7 u 2 = 7.
Sequence. A Sequence is a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details.
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The general term of an arithmetic sequence can be written in terms of its first term \(a_{1}\), common difference \(d\), and index \(n\) as follows: \(a_{n} = a_{1} + (n − 1) d\). An arithmetic series is the sum of the terms of an arithmetic sequence.
