Transcript
Page 1: 11X1 T14 02 geometric series (2011)

Geometric Series

Page 2: 11X1 T14 02 geometric series (2011)

Geometric Series An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

Page 3: 11X1 T14 02 geometric series (2011)

Geometric Series An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

Page 4: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

Page 5: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

Page 6: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

Page 7: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

Page 8: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 2

Page 9: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT

Page 10: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

Page 11: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

32, 8, 2, of termgeneral theand Find .. rige

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

Page 12: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

32, 8, 2, of termgeneral theand Find .. rige

4,2 ra

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

Page 13: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

32, 8, 2, of termgeneral theand Find .. rige

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

1 n

n arT 4,2 ra

Page 14: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

32, 8, 2, of termgeneral theand Find .. rige

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

1 n

n arT

142

n

4,2 ra

Page 15: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

32, 8, 2, of termgeneral theand Find .. rige

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

1 n

n arT

142

n

22

12

22

22

n

n

4,2 ra

Page 16: 11X1 T14 02 geometric series (2011)

Geometric Series

a

Tr 2

2

3

T

T

aT 1

32, 8, 2, of termgeneral theand Find .. rige

4,2 ra

An geometric series is a sequence of numbers in which each term after

the first is found by multiplying a constant amount to the previous

term.

The constant amount is called the common ratio, symbolised, r.

1

n

n

T

Tr

arT 22

3 arT 1 n

n arT

1 n

n arT

142

n

22

12

22

22

n

n 122 n

nT

Page 17: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

Page 18: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

Page 19: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar493 ar

Page 20: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar493 ar

72 r

Page 21: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar493 ar

72 r

7r

Page 22: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

493 ar

72 r

7r

Page 23: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

493 ar

72 r

7r

4,1 ra

Page 24: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

493 ar

72 r

7r

4,1 ra 141

n

nT

Page 25: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

493 ar

72 r

7r

4,1 ra 141

n

nT

Page 26: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

5004 1 n

493 ar

72 r

7r

4,1 ra 141

n

nT

Page 27: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

5004 1 n

493 ar

72 r

7r

4,1 ra 141

n

nT

500log4log 1 n

Page 28: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

5004 1 n

500log4log1 n

493 ar

72 r

7r

4,1 ra 141

n

nT

500log4log 1 n

Page 29: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

5004 1 n

500log4log1 n

48.5

48.41

n

n

493 ar

72 r

7r

4,1 ra 141

n

nT

500log4log 1 n

Page 30: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

5004 1 n

500log4log1 n

48.5

48.41

n

n

500 first term theis ,10246 T

493 ar

72 r

7r

4,1 ra 141

n

nT

500log4log 1 n

Page 31: 11X1 T14 02 geometric series (2011)

rTTii find ,49 and 7 If 42

7ar

(iii) find the first term of 1, 4, 16, … to

be greater than 500.

500nT

5004 1 n

500log4log1 n

48.5

48.41

n

n

500 first term theis ,10246 T

Exercise 6E; 1be, 2cf, 3ad, 5ac, 6c, 8bd, 9ac, 10ac, 15, 17,

18ab, 20a

493 ar

72 r

7r

4,1 ra 141

n

nT

500log4log 1 n


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