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=8x−2
y equals 8 x minus 2

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

y=2x−8

Answer 1

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

The sequence formula can be expanded as follows:

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

Now, we can see that this is of the form \( y = mx + b \), where \( m = 8 \) (the coefficient of \( n \)) and \( b = -2 \) (the constant term).

Now, let's compare it with the provided options:

1. \( y = 6x + 8 \)
2. \( y = 8x - 2 \)
3. \( y = 8x + 6 \)
4. \( y = 2x - 8 \)

The correct answer is:

**y = 8x - 2**

This matches the structure of the arithmetic sequence.