Download Sequences of Numbers

Sequences And Series
By the end of this lesson you will be able to explain/calculate the
following:
1. Arithmetic Sequences


A number sequence is a set of numbers
defined by a rule that is valid for positive
integers.
A number sequence is a function whose
domain is the set of positive integers.



Consider the illustrated tower of bricks.
The first row has three bricks, the second row
has four bricks, and the third row has five
bricks.
If un represents the number of bricks in row n
then u1 = 3, u2 = 4, u3 = 5, u4 = 6, .....
This sequence can be specified by:
1. listing terms
2. using words
3. using an explicit formula
4. a pictorial or graphical representation

1.
2.
3.
4.
An arithmetic sequence is a sequence of
numbers for which the difference between
successive terms is the same.
The first term of an arithmetic sequence is
referred to as ‘a ’.
The common difference between successive
terms is referred to as ‘d’.
tn is the term number
 for example, t6 refers to the 6th term in the
sequence.






un , Tn , tn , An can all be used to represent the
general term or nth term of a sequence.
The general term is defined for n = 1, 2, 3, ....
{un} represents the sequence that can be
generated by using un as the nth term.
+
{un} is a function, where n un, n
{2n + 1} generates the sequence 3, 5, 7, 9, ....
Written as: un = 2n +1
Now write the next 3 terms