11X1 T14 01 definitions & arithmetic series (2011)

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 term the: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 term the:nT

n termsfirst theof sum the: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 term the:nT

n termsfirst theof sum the: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 term the:nT

n termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

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 term the:nT

n termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

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 term the:nT

n termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

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 term the:nT

n termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

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 term the:nT

n termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

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 term the:nT

n termsfirst theof sum the:nS

find; ,2 .. 2 nTge n

5 Ti

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 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.

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.

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.general the

find; ,21 and 9 If .. 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.general the

find; ,21 and 9 If .. 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.general the

find; ,21 and 9 If .. 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 TTd

daT 2

daT 23

dnaTn 1

Arithmetic Series

aTd 2

23 TT

aT 1

term.general the

find; ,21 and 9 If .. 73 TTige

92 da216 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.general the

find; ,21 and 9 If .. 73 TTige

92 da216 da

3

124

d

d

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 TTd

daT 2

daT 23

dnaTn 1

Arithmetic Series

aTd 2

23 TT

aT 1

term.general the

find; ,21 and 9 If .. 73 TTige

92 da216 da

3

124

d

d

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 TTd

daT 2

daT 23

dnaTn 1

313 nTn

Arithmetic Series

aTd 2

23 TT

aT 1

term.general the

find; ,21 and 9 If .. 73 TTige

92 da216 da

3

124

d

d

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 TTd

daT 2

daT 23

dnaTn 1

313 nTn

n

n

3

333

100 Tii

100 Tii

300

1003

100 Tii

300

1003

(iii) the first term greater than 500

100 Tii

300

1003

(iii) the first term greater than 500

500nT

100 Tii

300

1003

(iii) the first term greater than 500

500nT

5003 n

100 Tii

300

1003

(iii) the first term greater than 500

500nT

5003 n

3

500n

100 Tii

300

1003

(iii) the first term greater than 500

500nT

5003 n

3

500n

167n

100 Tii

300

1003

(iii) the first term greater than 500

500nT

5003 n

3

500n

167n

500 first term theis ,501167 T

100 Tii

300

1003

(iii) the first term greater than 500

500nT

5003 n

3

500n

167n

500 first term theis ,501167 T

Exercise 6C; 1aceg, 2bdf, 3aceg, 5, 7bd, 10, 13b, 15

Exercise 6D; 1adg, 2c, 3bd, 6a, 7, 9bd, 13