11 x1 t14 02 geometric series (13)
TRANSCRIPT
![Page 1: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/1.jpg)
Geometric Series
![Page 2: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/2.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/3.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/4.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/5.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/6.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/7.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/8.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/9.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/10.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/11.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/12.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/13.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/14.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/15.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/16.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/17.jpg)
rTTii find ,49 and 7 If 42
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rTTii find ,49 and 7 If 42
7ar
![Page 19: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/19.jpg)
rTTii find ,49 and 7 If 42
7ar493 ar
![Page 20: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/20.jpg)
rTTii find ,49 and 7 If 42
7ar493 ar
72 r
![Page 21: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/21.jpg)
rTTii find ,49 and 7 If 42
7ar493 ar
72 r
7r
![Page 22: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/22.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/23.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/24.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/25.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/26.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/27.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/28.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/29.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/30.jpg)
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: 11 x1 t14 02 geometric series (13)](https://reader033.vdocuments.us/reader033/viewer/2022052906/55895d29d8b42a693f8b4644/html5/thumbnails/31.jpg)
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