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C1 Chapter 6 Arithmetic Series Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 7 th October 2013

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Types of sequences 2, 5, 8, 11, 14, … +3 This is a: Arithmetic Series ? Geometric Series ? 3, 6, 12, 24, 48, … ? ? 1, 1, 2, 3, 5, 8, … This is the Fibonacci Sequence. The terms follow a recurrence relation because each term can be generated using the previous ones. ?

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The fundamentals of sequences The position. ? ? ? ? ? ? ? ?

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Term-to-term and position-to-term ? ?

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1 st Term2 nd Term3 rd Term... ??? ?

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Find the requested term of the following sequences. 100 th term 50 th term 20 th term ??? ? ?? ? ? ?? ? ? ? ?

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Exercises ? ? ? ? 1 2 3 4

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The number of terms ? ? Add or subtract such that the numbers are now multiples of the common difference. Then divide.

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The number of terms How many terms? (work out in your head!) 1 2 3 4 5 ? ? ? ? ?

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? Let’s prove it! Find the sum of the first 30 terms of the following arithmetic sequences… 1 2 3 ? ? ?

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?

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Edexcel C1 Jan 2012 ? ? Exam Question

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Exercise 6F Q1a, c, e, g Q2a, c Q5, Q6, 8, 10

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What do these summations mean? ? ? ? This is commonly seen in exams.

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? ??

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More on recurrence relations There will occasionally be two series questions, one on nth term/sum of n terms, and the other on recurrence relations. Note that the sequence may not be arithmetic. Edexcel C1 May 2013 (Retracted) How would you say this in words? ? ? ? ?

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More on recurrence relations Edexcel C1 Jan 2012 ? ? ?

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12.3 – Analyze Geometric Sequences and Series. Geometric Sequence: Ratio of any term to the previous term is constant Common Ratio: Ratio each term is.

12.3 – Analyze Geometric Sequences and Series. Geometric Sequence: Ratio of any term to the previous term is constant Common Ratio: Ratio each term is.

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