Exercise 6 Page 155

We can represent an arithmetic sequence in different ways. We can do so by using a rule to define each term of the sequence, or do it graphically. We will try both of these one at a time.

Using Rules

We can represent an arithmetic sequence by using an explicit rule or a recursive rule.

Explicit Rule: Defines the n^(th) term as a function of its position number n. The general equation for a explicit rule is given below. f(n) = f(1) + d(n-1) In this equation f(1) is the first term of the sequence, while d represents the common difference.


Recursive Rule: Gives the first term of the sequence and defines the n^(th) term relating it to the previous ones. The general equation for a recursive rule is given below. f(n) = f(n-1) + d , for a givenf(1) In this equation f(1) is the first term of the sequence, while d represents the common difference.

Using a graph

We can represent a sequence using a graph as well. For this we can think of the position numbers as the x-coordinate values, and the terms as the y-coordinate values. Notice that as the position numbers can only be whole numbers, the graph will result in a series of unconnected points.