The document defines arithmetic series as a sequence of numbers where each term is found by adding a constant amount (called the common difference) to the previous term. It provides the general formula for an nth term in an arithmetic series as Tn = a + (n-1)d, where a is the first term and d is the common difference. As an example, it calculates the general term for a series where T3 = 9 and T7 = 21, finding the common difference d = 3 and first term a = 3, giving the formula Tn = 3n - 3. It is then asked to calculate the 100th term T100 for this series.

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
Tn : the nth term

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
Sn : the sum of the first n terms

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
Sn : the sum of the first n terms
e.g. Tn  n 2  2, find;

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
Sn : the sum of the first n terms
e.g. Tn  n 2  2, find;
i  T5

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
Sn : the sum of the first n terms
e.g. Tn  n 2  2, find;
i  T5  52  2
 27

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
Sn : 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. 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
Sn : 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. 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
Sn : 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. 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
Sn : 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. Arithmetic Series

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. ii  T100

33. ii  T100  3100
 300

34. ii  T100  3100 (iii) the first term greater than 500
 300

35. ii  T100  3100 (iii) the first term greater than 500
 300 Tn  500

36. ii  T100  3100 (iii) the first term greater than 500
 300 Tn  500
3n  500

37. ii  T100  3100 (iii) the first term greater than 500
 300 Tn  500
3n  500
500
n
3

38. ii  T100  3100 (iii) the first term greater than 500
 300 Tn  500
3n  500
500
n
3
n  167

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. 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