Transcript
Page 1: 11X1 T10 01 definitions & arithmetic series

Series & Applications

Page 2: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitions

Page 3: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a pattern

Page 4: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added together

Page 5: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

Page 6: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nT

Page 7: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

Page 8: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

Page 9: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

Page 10: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti27

252

Page 11: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti27

252

(ii) whether 42 is a term in the sequence

Page 12: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti27

252

(ii) whether 42 is a term in the sequence

242 2 n

Page 13: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti27

252

(ii) whether 42 is a term in the sequence

242 2 n

40402

nn

Page 14: 11X1 T10 01 definitions & arithmetic series

Series & ApplicationsDefinitionsSequence (Progression):a set of numbers that follow a patternSeries:a set of numbers added togethera:the first term

nth term the:nTn termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti27

252

(ii) whether 42 is a term in the sequence

242 2 n

40402

nn

, which is not an integerThus 42 is not a term

Page 15: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

Page 16: 11X1 T10 01 definitions & 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.

Page 17: 11X1 T10 01 definitions & 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.

The constant amount is called the common difference, symbolised, d.

Page 18: 11X1 T10 01 definitions & arithmetic series

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.

Page 19: 11X1 T10 01 definitions & arithmetic series

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.

Page 20: 11X1 T10 01 definitions & arithmetic series

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

Page 21: 11X1 T10 01 definitions & arithmetic series

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

Page 22: 11X1 T10 01 definitions & arithmetic series

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 TTddaT 2

Page 23: 11X1 T10 01 definitions & arithmetic series

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 TTddaT 2

daT 23

Page 24: 11X1 T10 01 definitions & arithmetic series

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 TTddaT 2

daT 23 dnaTn 1

Page 25: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 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 TTddaT 2

daT 23 dnaTn 1

Page 26: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 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 TTddaT 2

daT 23 dnaTn 1

Page 27: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 73 TTige

92 da216 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 TTddaT 2

daT 23 dnaTn 1

Page 28: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 73 TTige

92 da216 da

3124

dd

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 TTddaT 2

daT 23 dnaTn 1

Page 29: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 73 TTige

92 da216 da

3124

dd

3a

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 TTddaT 2

daT 23 dnaTn 1

Page 30: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 73 TTige

92 da216 da

3124

dd

3a

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 TTddaT 2

daT 23 dnaTn 1

313 nTn

Page 31: 11X1 T10 01 definitions & arithmetic series

Arithmetic Series

aTd 2

23 TT aT 1

term.general the

find;,21and 9If.. 73 TTige

92 da216 da

3124

dd

3a

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 TTddaT 2

daT 23 dnaTn 1

313 nTn

nn

3333

Page 32: 11X1 T10 01 definitions & arithmetic series

100 Tii

Page 33: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003

Page 34: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

Page 35: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

500nT

Page 36: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

500nT5003 n

Page 37: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

500nT5003 n

3500

n

Page 38: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

500nT5003 n

3500

n

167n

Page 39: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

500nT5003 n

3500

n

167n500first termtheis,501167 T

Page 40: 11X1 T10 01 definitions & arithmetic series

100 Tii 300

1003 (iii) the first term greater than 500

500nT5003 n

3500

n

167n500first 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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