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
S n : 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
S n : 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
S n : 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
S n : 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
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. 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. 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. 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. 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 Tn1
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 Tn1
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 Tn1
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 Tn1 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 Tn1 T3 a 2d
Tn a n 1d
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 Tn1 T3 a 2d
Tn a n 1d
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 Tn1 T3 a 2d
Tn a n 1d
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 Tn1 T3 a 2d
Tn a n 1d
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 Tn1 T3 a 2d
Tn a n 1d
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 Tn1 T3 a 2d
Tn a n 1d
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 Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9 Tn 3 n 13
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 Tn1 T3 a 2d
Tn a n 1d
e.g .i If T3 9 and T7 21, find;
the general term.
a 2d 9 Tn 3 n 13
a 6d 21 3 3n 3
4d 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 500
500
n
3
38. ii T100 3100 (iii) the first term greater than 500
300 Tn 500
3n 500
500
n
3
n 167
39. ii T100 3100 (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 3100 (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
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