Question

To show that arithmetic sequence formulas have the same structure as linear functions, choose the linear function equation that has the same structure as the arithmetic sequence an=6+(n−1)⋅8
𝑎
𝑛
=
6
+
(
𝑛
−
1
)
⋅
8
.

Answer 1

Write n as the input variable x and expand:
a_n = 6 + (n−1)·8 = 6 + 8n − 8 = 8n − 2.

So the corresponding linear function is f(x) = 8x − 2 (or y = 8x − 2), with slope 8 and y-intercept −2.