11 x1 t14 01 definitions & arithmetic series (2012)
TRANSCRIPT
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