Definition of a Sequence

Then the "next" term in the given sequence of numbers is 5: = 25.

Example 3.1 Find a function or formula that corresponds to the first three terms of the sequence

Solution

One function thai works is

Another is

Example 3.1 illustrates the general result that for any n numbers intended to describe a sequence, there is more than one function that can be used to generate the sequence of numbers given. In fact there are an infinite number of possibilities. Therefore such questions on IQ tests requesting one to fill in the next number of a sequence are poorly designed. If the respondent considering example 3.1 had in mind the equation (3,1), then she would offer 10 as the "next number" while if she had in mind the equation (3.2), she would offer 16 as the "next number."

A formal definition of a sequence follows, along with several examples.

A sequence is a function whose domain is ihe positive integers.

The following are examples of sequences:

I,

fin) -

2n

or

2,4, 6, 8, 10

(figure 3,1)

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