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Revision Topic 15: Algebra 2SequencesA linear sequence is one which goes up by the same amount each time.E.g. 5, 8, 11, 14, 17, is a linear sequence it goes up in 3s.E.g. 213, 11, 9, 7, 5, is a linear sequence it goes down in 2s.nth term formulaThe terms of a sequence can often be generated by a formula.Example: The formula for the nth term of a sequence is 4n + 5.a) Find the first 4 terms of the sequence.b) Which term of the sequence is 49.a) To get the first 4 terms of the sequence you have to replace n by 1, 2, 3, and 4.The 1st term of the sequence is 4 1 + 5 = 9The 2nd term of the sequence is 4 2 + 5 = 13The 3rd term of the sequence is 4 3 + 5 = 17The 4th term of the sequence is 4 4 + 5 = 21.b) To see which term of the sequence is 49 we solve: 4n + 5 = 49i.e 4n = 44i.e. n = 11The 11th term of the sequence is 49.Finding the nth term of a formulaThe formula for the nth term of a linear sequence is: n + Example: Find an expression for the nth number in the sequence 7, 12, 17, 22, 27.Solution: The sequence goes up in 5s.The term before 7

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