Compare the linear function and the arithmetic sequence below.
Linear Function:
x y
-1 10
0 14
1 18
2 22
The rate of change of the linear function is
The y-intercept of the linear function is
Arithmetic Sequence (Explicit formula):
an = 14 + 4(n−1)
The rate of change (common difference) of the arithmetic sequence is
The initial value of the arithmetic sequence is
The rate of change of this linear function is
the rate of change of this arithmetic sequence.
Arithmetic sequences
can be represented as a linear function.
The rate of change of the linear function is the same as the common difference of the arithmetic sequence. In this case, the rate of change is 4.
The y-intercept of the linear function is the initial value of the arithmetic sequence. In this case, the y-intercept is 10.
The rate of change (common difference) of the arithmetic sequence is 4.
The initial value of the arithmetic sequence is 14.
So the rate of change of the linear function (4) is the same as the rate of change of the arithmetic sequence (4). They both increase by 4 each time.