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+6
y equals 8 x plus 6

y=8x−2
y equals 8 x minus 2

y=6x+8

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 rearrange the formula into the form \( a_n = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting from the given formula:

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

We can distribute the 8:

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

Now, simplify it:

\[
a_n = 8n - 2
\]

This shows that the arithmetic sequence can be expressed in the form of a linear function where \( m = 8 \) (the coefficient of \( n \), or the slope) and \( b = -2 \) (the constant term).

Now, we need to find the linear function equation that matches this structure, specifically:

\[
y = 8x - 2
\]

So the correct response is:

**y = 8x - 2**