11X1 T14 01 definitions & arithmetic series (2011)

Series & Applications
Definitions

Definitions
Sequence (Progression):a set of numbers that follow a pattern

Definitions
Series:a set of numbers added together

Definitions
a:the first term

Definitions
a:the first term
Tn : the nth term

Definitions
a:the first term
Tn : the nth term
Sn : the sum of the first n terms

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;
i  T5

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;
i  T5  52  2
 27

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;
i  T5  52  2 (ii) whether 42 is a term in the sequence
 27

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;
 27 42  n 2  2

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;
 27 42  n 2  2
n 2  40
n  40

Definitions
a:the first term
Tn : the nth term
e.g. Tn  n 2  2, find;
 27 42  n 2  2
n 2  40
n  40 , which is not an integer
Thus 42 is not a 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.

Arithmetic Series

The constant amount is called the common difference, symbolised, d.

Arithmetic Series

d  T2  a

Arithmetic Series

d  T2  a
 T3  T2

Arithmetic Series

d  T2  a
 T3  T2
d  Tn  Tn1

Arithmetic Series

d  T2  a T1  a
 T3  T2
d  Tn  Tn1

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.
a  2d  9

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.
a  2d  9
a  6d  21

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.
a  2d  9
a  6d  21
4d  12
d 3

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.
a  2d  9
a  6d  21
4d  12
d  3 a  3

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.
a  2d  9 Tn  3  n  13
a  6d  21
4d  12
d  3 a  3

Arithmetic Series

d  T2  a T1  a
 T3  T2 T2  a  d
d  Tn  Tn1 T3  a  2d
Tn  a  n  1d
e.g.i  If T3  9 and T7  21, find;
the general term.
a  2d  9 Tn  3  n  13
a  6d  21  3  3n  3
4d  12  3n
d  3 a  3

ii  T100  3100
 300

ii  T100  3100 (iii) the first term greater than 500
 300

 300 Tn  500

 300 Tn  500
3n  500

 300 Tn  500
3n  500
500
n
3

 300 Tn  500
3n  500
500
n
3
n  167

 300 Tn  500
3n  500
500
n
3
n  167
T167  501, is the first term  500

 300 Tn  500
3n  500
500
n
3
n  167
T167  501, is the first term  500

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

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

11X1 T14 01 definitions & arithmetic series (2011)

More Related Content

What's hot (15)

Viewers also liked (10)

Similar to 11X1 T14 01 definitions & arithmetic series (2011) (20)

More from Nigel Simmons (20)

Recently uploaded (20)

11X1 T14 01 definitions & arithmetic series (2011)