11 x1 t14 01 definitions & arithmetic series (2012)

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  1. 1. Series & Applications
  2. 2. Series & ApplicationsDefinitions
  3. 3. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a pattern
  4. 4. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added together
  5. 5. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term
  6. 6. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth term
  7. 7. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n terms
  8. 8. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.g. Tn n 2 2, find;
  9. 9. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.g. Tn n 2 2, find; i T5
  10. 10. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.g. Tn n 2 2, find; i T5 52 2 27
  11. 11. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.g. Tn n 2 2, find; i T5 52 2(ii) whether 42 is a term in the sequence 27
  12. 12. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.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. 13. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.g. Tn n 2 2, find; i T5 52 2(ii) whether 42 is a term in the sequence 27 42 n 2 2n 2 40n 40
  14. 14. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth termSn : the sum of the first n termse.g. Tn n 2 2, find; i T5 52 2(ii) whether 42 is a term in the sequence 27 42 n 2 2n 2 40n 40 , which is not an integer Thus 42 is not a term
  15. 15. Arithmetic Series
  16. 16. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe first is found by adding a constant amount to the previous term.
  17. 17. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe first is found by adding a constant amount to the previous term.The constant amount is called the common difference, symbolised, d.
  18. 18. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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. 19. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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. 20. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 T2d Tn Tn1
  21. 21. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 T2d Tn Tn1
  22. 22. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 dd Tn Tn1
  23. 23. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 dd Tn Tn1T3 a 2d
  24. 24. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 dd Tn Tn1T3 a 2d Tn a n 1d
  25. 25. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.
  26. 26. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.a 2d 9
  27. 27. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.a 2d 9 a 6d 21
  28. 28. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.a 2d 9 a 6d 214d 12d 3
  29. 29. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.a 2d 9 a 6d 214d 12 d 3 a 3
  30. 30. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.a 2d 9 Tn 3 n 13 a 6d 214d 12 d 3 a 3
  31. 31. Arithmetic SeriesAn arithmetic series is a sequence of numbers in which each term afterthe 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 d d Tn Tn1T3 a 2dTn a n 1de.g.i If T3 9 and T7 21, find;the general term.a 2d 9 Tn 3 n 13 a 6d 21 3 3n 34d 12 3n d 3 a 3
  32. 32. ii T100
  33. 33. ii T100 3100 300
  34. 34. ii T100 3100 (iii) the first term greater than 500 300
  35. 35. ii T100 3100 (iii) the first term greater than 500 300 Tn 500
  36. 36. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500
  37. 37. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500500n 3
  38. 38. ii T100 3100 (iii) the first term greater than 500 300 Tn 5003n 500 500 n3 n 167
  39. 39. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500 500n3 n 167 T167 501, is the first term 500
  40. 40. ii T100 3100(iii) the first term greater than 500 300Tn 5003n 500500 n 3n 167T167 501, is the first term 500 Exercise 6C; 1aceg, 2bdf, 3aceg, 5, 7bd, 10, 13b, 15 Exercise 6D; 1adg, 2c, 3bd, 6a, 7, 9bd, 13