# 11 x1 t14 01 definitions & arithmetic series (2012)

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- 1. Series & Applications
- 2. Series & ApplicationsDefinitions
- 3. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a pattern
- 4. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added together
- 5. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term
- 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. 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. 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. 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. 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. 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. 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. 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. 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. Arithmetic Series
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 500 3n 500
- 37. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500500n 3
- 38. ii T100 3100 (iii) the first term greater than 500 300 Tn 5003n 500 500 n3 n 167
- 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. 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