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) 𝑎 𝑛 = 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

Linear function:
- Rate of change (slope) = 4
- y-intercept = 14
(so the line is y = 4x + 14)

Arithmetic sequence an = 10 + 4(n − 1):
- Common difference (rate of change) = 4
- First term a1 = 10
(also an = 6 + 4n)

Comparison:
- The rate of change of the linear function is equal to the rate of change of the arithmetic sequence (both are 4).
- Yes — an arithmetic sequence is a linear function of n. In fact an = f(n − 2) where f(x) = 4x + 14 (equivalently an = 6 + 4n).