1. C2: Geometric Series Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 24 th September 2013

2. Types of series 2, 5, 8, 11, 14, … +3 This is a: Arithmetic Series ? Geometric Series ? 3, 6, 12, 24, 48, … ? ?

3. Common Ratio 1 2 3 4 5 6 7 ? ? ? ? ? ? ?

4. Common Ratio Exam Question May 2013 (Retracted) Hint for (a): the common ratio between the first and second terms, and the second and third terms, is the same. a b ? ?

5. Arithmetic SeriesGeometric Series Determine the following: 3, 6, 12, 24, … 40, -20, 10, -5, … ? ? ? ??

6. Another Common Ratio Example ?

7. Missing information The second term of a geometric sequence is 4 and the 4 th term is 8. The common ratio is positive. Find the exact values of: a)The common ratio. b)The first term. c)The 10 th term. The second term of a geometric sequence is 4 and the 4 th term is 8. The common ratio is positive. Find the exact values of: a)The common ratio. b)The first term. c)The 10 th term. ?

8. ?

9. Exam Question Edexcel June 2010 ? ? ? ? ?

10. Arithmetic SeriesGeometric Series ? ? Technically you could be asked in an exam the proof of the sum of a geometric series (it once came up!) So let’s prove it…

11. Geometric Series Find the sum of the first 10 terms. ? ? ? ? ? ? ? ?

12. Summation Notation ? ? ? ?

13. Harder Questions: Type 1 ? ?

14. Exercise 7D 1 2 4 5 6 ? ? ? ? ? ? ? ? ? ?

15. Different types of series 1 + 2 + 4 + 8 + 16 +... What can you say about the sum of each series up to infinity? 1 + 2 + 3 + 4 + 5 +... 1 + 0.5 + 0.25 + 0.125 +... This is divergent – the sum of the values tends towards infinity. This is convergent – the sum of the values tends towards a fixed value, in this case 2. This is divergent. This is known as the Harmonic Series Just for fun... ? ? ? ? ?

16. Sum to Infinity ? ?

17. Examples ? ? ?? ? ? ? ? ? ? ? ?

18. A somewhat esoteric Futurama joke explained

20. Another Example ? ?

21. Edexcel May 2011 ? ? ? ?

22. Exercises Exercise 7D Q6, 7 Exercise 7E Q8 Exercise 7F Q10