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A sequence is written as:
Notes
(i) A sequence which goes on forever is called an infinite sequence.
A sequence which stops is called a finite sequence.
(ii)
= the first term = the value of the object in the first place.
= the second term = the value of the object in the second place etc.Example 1
In the sequence
= the value of the object in the first place.
= the value of the object in the fourth place(iii) The General term
If you know the general term of a sequence you can work out any other term.
Example 2
If the general term of a sequence is given by
Find
Solution
(iv)
can be any function of nExample 3
If
find 
.Solution
(a) The Sum of the first n terms
.Students often get un and
mixed up. So, be very clear.
the value of the object in the 
place.
the value of the object in the 
place
= the sum of the first 
terms=
Example 4
For the sequence:
find 
.Solution
(b) Relationship between
and
Notes: (i) This is a very important result as it is true for all sequences.
(ii) Given
for any sequence you can find 
.(iii) In a later article we will see how to get
from 
.Example 5
If
for a sequence find 
Solution
Example 6
If
for a sequence find 
Show that
Solution
Example 7
If
show that 
Solution
Example 8
If
show that 
Solution
