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
nth termthe:nT

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
nth termthe:nT
n termsfirsttheofsumthe:nS

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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n

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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n
  5Ti

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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n
  5Ti
27
252



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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n
  5Ti
27
252

 (ii) whether 42 is a term in the sequence

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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n
  5Ti
27
252

 (ii) whether 42 is a term in the sequence
242 2
 n

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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n
  5Ti
27
252

 (ii) whether 42 is a term in the sequence
242 2
 n
40
402


n
n

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
nth termthe:nT
n termsfirsttheofsumthe:nS
find;,2.. 2
 nTge n
  5Ti
27
252

 (ii) whether 42 is a term in the sequence
242 2
 n
40
402


n
n
, 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 after
the 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 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
aTd  2
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.

19. Arithmetic Series
aTd  2
23 TT 
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.

20. Arithmetic Series
aTd  2
23 TT 
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.
1 nn TTd

21. Arithmetic Series
aTd  2
23 TT 
aT 1
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.
1 nn TTd

22. Arithmetic Series
aTd  2
23 TT 
aT 1
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.
1 nn TTd
daT 2

23. Arithmetic Series
aTd  2
23 TT 
aT 1
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.
1 nn TTd
daT 2
daT 23 

24. Arithmetic Series
aTd  2
23 TT 
aT 1
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1

25. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1

26. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
92  da
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1

27. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
92  da
216  da
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1

28. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
92  da
216  da
3
124


d
d
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1

29. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
92  da
216  da
3
124


d
d
3a
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1

30. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
92  da
216  da
3
124


d
d
3a
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1
 313  nTn

31. Arithmetic Series
aTd  2
23 TT 
aT 1
 
term.generalthe
find;,21and9If.. 73  TTige
92  da
216  da
3
124


d
d
3a
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.
1 nn TTd
daT 2
daT 23 
 dnaTn 1
 313  nTn
n
n
3
333



32.   100Tii

33.   100Tii  
300
1003



34.   100Tii  
300
1003

 (iii) the first term greater than 500

35.   100Tii  
300
1003

 (iii) the first term greater than 500
500nT

36.   100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n

37.   100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n

38.   100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n
167n

39.   100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n
167n
500first termtheis,501167 T

40.   100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n
167n
500first termtheis,501167 T
Exercise 6C; 1aceg, 2bdf, 3aceg, 5, 7bd, 10, 13b, 15
Exercise 6D; 1adg, 2c, 3bd, 6a, 7, 9bd, 13