compare the linear function and the arithmetic sequence below.
linear function
x
-1,0,1,2
y
10,14,18,22
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 sequence _ can be represented as a linear function
The rate of change of the linear function can be found by calculating the difference in the y-values for any two points. In this case, taking any two points (0, 14) and (1, 18), the rate of change is (18-14)/(1-0) = 4.
The y-intercept of the linear function is the y-value when x=0. In this case, when x=0, y=14.
The rate of change (common difference) of the arithmetic sequence can be found by subtracting any two terms. In this case, taking the first two terms (10 and 14), the common difference is 14 - 10 = 4.
The initial value of the arithmetic sequence is the value of the first term, which is 14.
The rate of change of the linear function (4) is the same as the rate of change (common difference) of the arithmetic sequence (4).
An arithmetic sequence can be represented as a linear function, where the terms of the sequence are the y-values and the sequence numbers are the x-values. In this case, the explicit formula for the arithmetic sequence is an=14+4(n-1), which can be simplified to y=4x+10.