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.
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The rate of change of the linear function is the difference in y-values divided by the difference in x-values. In this case, the rate of change is (18-14)/(1-0) = 4.
The y-intercept of the linear function is the value of y when x=0. In this case, the y-intercept is 14.
The rate of change (common difference) of the arithmetic sequence is the constant difference between consecutive terms. In this case, the rate of change is 4.
The initial value of the arithmetic sequence is the value of the sequence when n=1. In this case, the initial value is 14.
The rate of change of the linear function is the same as the rate of change of the arithmetic sequence since they both have a rate of change of 4.
Arithmetic sequences can be represented as a linear function using the explicit formula for the nth term. In this case, the nth term of the arithmetic sequence is given by an = 14 + 4(n-1), which can also be written as a linear function y = 4x + 14.