Question

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 = 10+ 4(n−1)


The rate of change (common difference) of the arithmetic sequence is

The first 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.

Answer 1

- Rate of change of the linear function: 4
- y-intercept of the linear function: 14 (so y = 4x + 14)

- Rate of change (common difference) of the arithmetic sequence an = 10 + 4(n−1): 4
- First value (a1) of the arithmetic sequence: 10 (since a1 = 10 + 4·0 = 10)

The rate of change of this linear function is equal to the rate of change of this arithmetic sequence (both are 4).

Yes — arithmetic sequences can be represented by linear functions. (Here an = 10 + 4(n−1) = 4n + 6; if you set n = x + 2 the sequence values match y = 4x + 14 from the table.)