11 x1 t14 01 definitions & arithmetic series (2013)

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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 nth termthe:nT
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n 5Ti
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n 5Ti 27 252
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n 5Ti 27 252 (ii) whether 42 is a term in the sequence
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n 5Ti 27 252 (ii) whether 42 is a term in the sequence 242 2 n
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n 5Ti 27 252 (ii) whether 42 is a term in the sequence 242 2 n 40 402 n n
  • 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 nth termthe:nT n termsfirsttheofsumthe:nS find;,2.. 2 nTge n 5Ti 27 252 (ii) whether 42 is a term in the sequence 242 2 n 40 402 n n , which is not an integer Thus 42 is not a term
  • 15. Arithmetic Series
  • 16. Arithmetic SeriesAn 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 SeriesAn 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 aTd 2 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.
  • 19. Arithmetic Series aTd 2 23 TT 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.
  • 20. Arithmetic Series aTd 2 23 TT 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. 1 nn TTd
  • 21. Arithmetic Series aTd 2 23 TT aT 1 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. 1 nn TTd
  • 22. Arithmetic Series aTd 2 23 TT aT 1 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. 1 nn TTd daT 2
  • 23. Arithmetic Series aTd 2 23 TT aT 1 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. 1 nn TTd daT 2 daT 23
  • 24. Arithmetic Series aTd 2 23 TT aT 1 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. 1 nn TTd daT 2 daT 23 dnaTn 1
  • 25. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 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. 1 nn TTd daT 2 daT 23 dnaTn 1
  • 26. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 92 da 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. 1 nn TTd daT 2 daT 23 dnaTn 1
  • 27. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 92 da 216 da 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. 1 nn TTd daT 2 daT 23 dnaTn 1
  • 28. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 92 da 216 da 3 124 d d 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. 1 nn TTd daT 2 daT 23 dnaTn 1
  • 29. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 92 da 216 da 3 124 d d 3a 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. 1 nn TTd daT 2 daT 23 dnaTn 1
  • 30. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 92 da 216 da 3 124 d d 3a 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. 1 nn TTd daT 2 daT 23 dnaTn 1 313 nTn
  • 31. Arithmetic Series aTd 2 23 TT aT 1 term.generalthe find;,21and9If.. 73 TTige 92 da 216 da 3 124 d d 3a 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. 1 nn TTd daT 2 daT 23 dnaTn 1 313 nTn n n 3 333
  • 32. 100Tii
  • 33. 100Tii 300 1003
  • 34. 100Tii 300 1003 (iii) the first term greater than 500
  • 35. 100Tii 300 1003 (iii) the first term greater than 500 500nT
  • 36. 100Tii 300 1003 (iii) the first term greater than 500 500nT 5003 n
  • 37. 100Tii 300 1003 (iii) the first term greater than 500 500nT 5003 n 3 500 n
  • 38. 100Tii 300 1003 (iii) the first term greater than 500 500nT 5003 n 3 500 n 167n
  • 39. 100Tii 300 1003 (iii) the first term greater than 500 500nT 5003 n 3 500 n 167n 500first termtheis,501167 T
  • 40. 100Tii 300 1003 (iii) the first term greater than 500 500nT 5003 n 3 500 n 167n 500first termtheis,501167 T Exercise 6C; 1aceg, 2bdf, 3aceg, 5, 7bd, 10, 13b, 15 Exercise 6D; 1adg, 2c, 3bd, 6a, 7, 9bd, 13