From Arithmetic Sequences to Linear Relations

Arithmetic Sequence as a Function

An arithmetic sequence is a function.

The input of an arithmetic sequence is the place value: that is, the natural numbers. The output is the term value.

The calculation that happens on the input is the ‘general term’ – multiply by the common difference, add or subtract to fit the sequence.

Notice that when we graph an arithmetic sequence, the points are colinear (lie on a line) although we don’t draw the line as there are no points ‘in between’ the points drawn on the applet.

Linear Relations

The following sets of points are also functions – a set of ordered pairs whereby for each element in the first place (domain) there is exactly one element in the second place (range).

When graphed, these sets of points are also colinear.