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Series & Applications
Series & Applications
Definitions
Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
Series & Applications
Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
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
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
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
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
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


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
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
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
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
Arithmetic Series
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.
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.
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.
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.
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
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
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
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 
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
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
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
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
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
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
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
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


  100Tii
  100Tii  
300
1003


  100Tii  
300
1003

 (iii) the first term greater than 500
  100Tii  
300
1003

 (iii) the first term greater than 500
500nT
  100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
  100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n
  100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n
167n
  100Tii  
300
1003

 (iii) the first term greater than 500
500nT
5003 n
3
500
n
167n
500first termtheis,501167 T
  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

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11 x1 t14 01 definitions & arithmetic series (2013)

  • 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
  • 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  
  • 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