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C1 Chapter 6 Arithmetic Series Dr J Frost Last modified: 7 th October 2013.

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Presentation on theme: "C1 Chapter 6 Arithmetic Series Dr J Frost Last modified: 7 th October 2013."— Presentation transcript:

1 C1 Chapter 6 Arithmetic Series Dr J Frost Last modified: 7 th October 2013

2 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. ?

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

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

5 1 st Term2 nd Term3 rd Term... ??? ?

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

7 Exercises ? ? ? ?

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

9 The number of terms How many terms? (work out in your head!) ? ? ? ? ?

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

11 ?

12 Edexcel C1 Jan 2012 ? ? Exam Question

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

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

15 ? ??

16 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? ? ? ? ?

17 More on recurrence relations Edexcel C1 Jan 2012 ? ? ?


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