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# Edexcel A-level Maths Introduction to sequences

A sequence is an ordered list of numbers that can be described by a specific rule. Each number in a sequence is, in turn, called a term of the sequence and each term occupies a position in the sequence.

The term to term rule of a sequence describes how to get from one term to the next in the sequence. To find the term to term rule, start at the first term and look for a pattern in moving between consecutive terms. From the term to term rule and the first term of a sequence the position to term rule, or general rule, can be worked out and used to find the nth term of a sequence, that is the term at position n where n is any position in a sequence.

A series is the sum of the terms of a sequence up to its nth term. It is denoted by Sn and is expressed as:

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Given the sequence Un = 2n, is the series Sā = 2 + 4 + 6 + 8 ā 10 + 12 a series for the sequence Un?

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Find Sā for the sequence Un = 2n ā 1.

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