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 Description  
 Sequence:  A pattern involving an ordered arrangement of numbers, geometric figures, letters, or other objects.

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?