2. AS Core Maths - TAM Online Session 5: Sequences & Series A warm-up question before we get started…

3. A RI THM ETIC PROGR ESSION G EO METR ICSERIES 51 is the 6 th pentagonal number. What is the 100 th pentagonal number?

4. Session content  Sequences  Recurrence relations  Sigma notation  Arithmetic Progressions  Geometric Progressions NB: This is content based on chapter 7 in the AS Core textbook

5. Sequences

6. Recurrence Relations

7. Sigma Notation

8. 45 21 -80 24

9. Arithmetic Sequence

10. Arithmetic Series

12. Arithmetic Progressions & Series

13. APs: the formulae

14. Typical APs Exam Question (Core 2 Jan 07 - Q8 [5 marks]) The 7 th term of an arithmetic progression is 6. The sum of the first 10 terms of the progression is 30. Find the 5 th term of the progression.

16. Geometric Progressions & Series

17. GPs: the formulae

18. AP or GP?

19. Typical GPs Exam Question Find two different geometric progressions with second term 18 and fourth term 2. Find the sum of the first 100 terms in each case.

20. Sum to infinity of a geometric series

22. Infinite GPs: the formula

23. Typical Infinite GPs Exam Question (Core 2 Jan 08 - Q8 [5 marks]) The second term of a geometric progression is 18 and the fourth term is 2. The common ratio is positive. Find the sum to infinity of this progression.

24. Session content check  Sequences  Recurrence relations  Sigma notation  Arithmetic Progressions  Geometric Progressions

25. AQA Core 2 Jun 12 – Q1 [5 marks]

26. MEI Core 2 Jan 09 - Q6 [5 marks]

27. OCR Core 2 Jun 12 – Q5 [8 marks]

28. MEI Core 2 Jun 08 - Q2 [3 marks]

29. MEI Core 2 Jun 08 - Q8 [5 marks] The 11 th term of an arithmetic progression is 1. The sum of the first ten terms is 120. Find the 4 th term.

30. MEI Core 2 Jun 09 - Q11(i) [5 marks]

31. MEI Core 2 Jun 09 - Q11(ii) [7 marks]