# 11X1 T14 01 definitions & arithmetic series (2011)

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<ol><li> 1. Series & Applications </li><li> 2. Series & ApplicationsDefinitions </li><li> 3. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a pattern </li><li> 4. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added together </li><li> 5. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term </li><li> 6. Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first termTn : the nth term </li><li> 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 </li><li> 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; </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 15. Arithmetic Series </li><li> 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. </li><li> 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. </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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. </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 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 </li><li> 32. ii T100 </li><li> 33. ii T100 3100 300 </li><li> 34. ii T100 3100 (iii) the first term greater than 500 300 </li><li> 35. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 </li><li> 36. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500 </li><li> 37. ii T100 3100 (iii) the first term greater than 500 300 Tn 500 3n 500500n 3 </li><li> 38. ii T100 3100 (iii) the first term greater than 500 300 Tn 5003n 500 500 n3 n 167 </li><li> 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 </li><li> 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</li></ol>