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=2x−8
y equals 2 x minus 8

y=8x−2
y equals 8 x minus 2

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

y=8x+6

Answer 1

To show that the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \) has the same structure as a linear function, we can first rearrange the arithmetic sequence formula into a more standard form.

Starting with the given equation:

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

We can expand this:

\[
a_n = 6 + 8n - 8
\]

Now simplifying this gives:

\[
a_n = 8n - 2
\]

This is now in the form of a linear function \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Comparing it with the provided options, we see that:

\[
y = 8x - 2
\]

matches the structure of our derived equation \( a_n = 8n - 2 \).

Therefore, the correct choice is:

**y = 8x - 2**