# 11X1 T14 01 definitions & arithmetic series (2010)

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- 1. Series & Applications

2. Series & Applications Definitions 3. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern 4. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together 5. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term 6. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term 7. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms 8. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find; 9. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find;i T5 10. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find;i T5 52 2 27 11. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find;i T5 52 2(ii) whether 42 is a term in the sequence 27 12. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find;i T5 52 2(ii) whether 42 is a term in the sequence 27 42 n 2 2 13. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find;i T5 52 2(ii) whether 42 is a term in the sequence 27 42 n 2 2 n 2 40 n 40 14. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together a:the first term Tn : the nth term Sn : the sum of the first n terms e.g. Tn n 2 2, find;i T5 52 2(ii) whether 42 is a term in the sequence 27 42 n 2 2 n 2 40 n 40 , which is not an integerThus 42 is not a term 15. Arithmetic Series 16. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term. 17. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. 18. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a 19. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a T3 T2 20. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a T3 T2 d Tn Tn1 21. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a T1 a T3 T2 d Tn Tn1 22. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a T1 a T3 T2T2 a d d Tn Tn1 23. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a T1 a T3 T2T2 a d d Tn Tn1T3 a 2d 24. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 a T1 a T3 T2T2 a d d Tn Tn1T3 a 2dTn a n 1d 25. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. 26. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. a 2d 9 27. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. a 2d 9a 6d 21 28. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. a 2d 9a 6d 21 4d 12 d 3 29. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. a 2d 9a 6d 21 4d 12d 3 a 3 30. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. a 2d 9 Tn 3 n 13a 6d 21 4d 12d 3 a 3 31. Arithmetic Series An arithmetic series is a sequence of numbers in which each term after the first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d. d T2 aT1 a T3 T2 T2 a dd Tn Tn1T3 a 2d Tn a n 1d e.g.i If T3 9 and T7 21, find; the general term. a 2d 9 Tn 3 n 13a 6d 21 3 3n 3 4d 12 3nd 3 a 3 32. ii T100 33. ii T100 3100 300 34. ii T100 3100 (iii) the first term greater than 500 300 35. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 36. ii T100 3100 (iii) the first term greater than 500 300 Tn 5003n 500 37. ii T100 3100 (iii) the first term greater than 500 300 Tn 5003n 500 500 n3 38. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500500n 3n 167 39. ii T100 3100 (iii) the first term greater than 500 300 Tn 5003n 500500 n 3n 167T167 501, is the first term 500 40. ii T100 3100(iii) the first term greater than 500 300Tn 500 3n 500 500n3 n 167 T167 501, is the first term 500Exercise 6C; 1aceg, 2bdf, 3aceg, 5, 7bd, 10, 13b, 15 Exercise 6D; 1adg, 2c, 3bd, 6a, 7, 9bd, 13