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=6x+8
y equals 6 x plus 8

y=2x−8
y equals 2 x minus 8

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

y=8x−2
y equals 8 x minus 2

Answer 1

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

The formula can be rewritten as:

\[
a_n = 6 + 8(n - 1) = 6 + 8n - 8 = 8n - 2
\]

This gives us the linear function in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In this case, the linear function can be expressed as:

\[
y = 8n - 2
\]

Thus, the correct choice from your options is:

**y = 8x - 2.**