The individual numbers, figures, or letters in the sequence are called the terms of the sequence. Typically, only the first 3 or 4 terms of a sequence are
listed, followed by an ellipsis (three periods which mean "and so on"). The
following table shows several numerical sequences of the counting numbers
(1,2,3,4,…)
Sequence 
Name of Sequence 
2, 4, 6, 8, … 
the even (counting/natural)
numbers 
1, 3, 5, 7, … 
the odd (counting/natural)
numbers 
1, 4, 9, 16, … 
the square (counting/natural)
numbers 

the powers of 7 
1, 1, 2, 3, 5, 8, … 
the Fibonacci sequence 
5, 10, 15, … 
an arithmetic
sequence 
5, 10, 20, 40, … 
a geometric
sequence 
The key to continuing a sequence is to look for a pattern. What is the common rule that
gets us from one term to the next?
Numerical sequences can be classified according to the method
used to get from one term to the next. For example, if we add a constant
as we move from one term to the next, the sequence is called an arithmetic
sequence (in the arithmetic sequence in the table above, we add 5 to each term to
get the next term). If we multiply by a constant as we move from one term
to the next, the sequence is called a geometric sequence (in the
geometric sequence in the table above, we multiply each term by 2 to get the next
term.
We can also look for patterns in sequences of geometric
figures. Consider the following figures. Can you identify the pattern and extend
the sequence by giving the next 3 terms?
