11 x1 t14 01 definitions & arithmetic series (2013)
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TRANSCRIPT
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Series & Applications
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Series & Applications Definitions
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Series & Applications Definitions
Sequence (Progression):a set of numbers that follow a pattern
![Page 4: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/4.jpg)
Series & Applications Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
![Page 5: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/5.jpg)
Series & Applications Definitions
Sequence (Progression):a set of numbers that follow a pattern
Series:a set of numbers added together
a:the first term
![Page 6: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/6.jpg)
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
![Page 7: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/7.jpg)
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
![Page 8: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/8.jpg)
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
![Page 9: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/9.jpg)
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
![Page 10: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/10.jpg)
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
![Page 11: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/11.jpg)
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
![Page 12: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/12.jpg)
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
![Page 13: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/13.jpg)
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
![Page 14: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/14.jpg)
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
![Page 15: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/15.jpg)
Arithmetic Series
![Page 16: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/16.jpg)
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.
![Page 17: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/17.jpg)
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.
![Page 18: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/18.jpg)
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: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/19.jpg)
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: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/20.jpg)
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: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/21.jpg)
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: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/22.jpg)
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
![Page 23: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/23.jpg)
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
![Page 24: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/24.jpg)
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
![Page 25: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/25.jpg)
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
![Page 26: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/26.jpg)
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
![Page 27: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/27.jpg)
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
![Page 28: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/28.jpg)
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
![Page 29: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/29.jpg)
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
![Page 30: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/30.jpg)
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
![Page 31: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/31.jpg)
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
![Page 32: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/32.jpg)
100 Tii
![Page 33: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/33.jpg)
100 Tii
300
1003
![Page 34: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/34.jpg)
100 Tii
300
1003
(iii) the first term greater than 500
![Page 35: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/35.jpg)
100 Tii
300
1003
(iii) the first term greater than 500
500nT
![Page 36: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/36.jpg)
100 Tii
300
1003
(iii) the first term greater than 500
500nT
5003 n
![Page 37: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/37.jpg)
100 Tii
300
1003
(iii) the first term greater than 500
500nT
5003 n
3
500n
![Page 38: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/38.jpg)
100 Tii
300
1003
(iii) the first term greater than 500
500nT
5003 n
3
500n
167n
![Page 39: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/39.jpg)
100 Tii
300
1003
(iii) the first term greater than 500
500nT
5003 n
3
500n
167n
500 first term theis ,501167 T
![Page 40: 11 x1 t14 01 definitions & arithmetic series (2013)](https://reader034.vdocuments.us/reader034/viewer/2022051616/5538352c550346592f8b46e7/html5/thumbnails/40.jpg)
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