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# 11X1 T10 01 definitions & arithmetic series

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### 11X1 T10 01 definitions & arithmetic series

1. 1. Series & Applications
2. 2. Series & Applications Definitions
3. 3. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern
4. 4. Series & Applications Definitions Sequence (Progression):a set of numbers that follow a pattern Series:a set of numbers added together
5. 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. 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. 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 S n : the sum of the first n terms
8. 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 S n : the sum of the first n terms e.g . Tn  n 2  2, find;
9. 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 S n : the sum of the first n terms e.g . Tn  n 2  2, find; i  T5
10. 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 S n : the sum of the first n terms e.g . Tn  n 2  2, find; i  T5  52  2  27
11. 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 S n : 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. 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 S n : 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. 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 S n : 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. 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 S n : 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 integer Thus 42 is not a term
15. 15. Arithmetic Series
16. 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. 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. 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. 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. 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  Tn1
21. 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  Tn1
22. 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  T2 T2  a  d d  Tn  Tn1
23. 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  T2 T2  a  d d  Tn  Tn1 T3  a  2d
24. 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  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d
25. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term.
26. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term. a  2d  9
27. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term. a  2d  9 a  6d  21
28. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term. a  2d  9 a  6d  21 4d  12 d 3
29. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term. a  2d  9 a  6d  21 4d  12 d  3 a  3
30. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term. a  2d  9 Tn  3  n  13 a  6d  21 4d  12 d  3 a  3
31. 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  a T1  a  T3  T2 T2  a  d d  Tn  Tn1 T3  a  2d Tn  a  n  1d e.g .i  If T3  9 and T7  21, find; the general term. a  2d  9 Tn  3  n  13 a  6d  21  3  3n  3 4d  12  3n d  3 a  3
32. 32. ii  T100
33. 33. ii  T100  3100  300
34. 34. ii  T100  3100 (iii) the first term greater than 500  300
35. 35. ii  T100  3100 (iii) the first term greater than 500  300 Tn  500
36. 36. ii  T100  3100 (iii) the first term greater than 500  300 Tn  500 3n  500
37. 37. ii  T100  3100 (iii) the first term greater than 500  300 Tn  500 3n  500 500 n 3
38. 38. ii  T100  3100 (iii) the first term greater than 500  300 Tn  500 3n  500 500 n 3 n  167
39. 39. ii  T100  3100 (iii) the first term greater than 500  300 Tn  500 3n  500 500 n 3 n  167 T167  501, is the first term  500
40. 40. ii  T100  3100 (iii) the first term greater than 500  300 Tn  500 3n  500 500 n 3 n  167 T167  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