An arithmetic sequence is characterized by the fact that there is a common difference between consecutive terms. Arithmetic sequences can be written in a standard formula.
a_n=a_1+(n-1)d
Note that this is a linear function. If we think of a_n as the y values and n as the x values, then we can think of d as the slope and of a_1 as the y-intercept. Our function then looks very similar to the slope-intercept form.
y=b+(x-1)m
Additionally, in an arithmetic sequence, n must be whole numbers.
First term:& n=1
Second term:& n=2
Third term:& n=3
As with any function where the domain is limited to positive integers, the domain is discrete. In general, an arithmetic sequence looks similar to the graph shown below.
