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 .(1 point)
Responses

y=8x−2
y equals 8 x minus 2

y=2x−8
y equals 2 x minus 8

y=6x+8
y equals 6 x plus 8

y=8x+6

Answer 1

To compare the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \) with a linear function, we can rewrite the arithmetic sequence formula in a more recognizable linear form.

Starting with:
\[
a_n = 6 + (n - 1) \cdot 8
\]

Distribute the 8:
\[
a_n = 6 + 8n - 8
\]

Combine like terms:
\[
a_n = 8n - 2
\]

Now, we can see that the arithmetic sequence can be represented as a linear function:
\[
y = 8x - 2
\]

Thus, the correct choice is:
\[
\text{y = 8x - 2}
\]