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OCR GCSE Maths Introduction to sequences 1. Basics of sequences
2. Generating terms in a sequence

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. 1

Consider the sequence {2, 4, 6, 8, 10, 12}. What is the position to term rule describing the even numbers sequence? 2

Consider the sequence {17, 15, 13, 11, 9, 7, 5, 3, 1}. What is the seventh term of the sequence? 3

Adam notices he at 2 apples two weeks ago, 4 apples the week after and 6 apples this week. What is the 2nd term of the sequence of apples? 4

Consider the sequence {3, 5, 7, 9, 11, 13, 15}. What is the nth term, or general rule, of the odd number sequence? 5

Consider the sequence {1, 3, 1000, 5, π, −17, −29}. Can the list be called a sequence? Explain your answer. End of page