Question

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=8x+6
y equals 8 x plus 6

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

y=2x−8

Answer 1

To determine which linear function has the same structure as the arithmetic sequence given by \( a_n = 6 + (n-1) \cdot 8 \), let's first rewrite the arithmetic sequence formula into a more recognizable linear form.

The formula can be simplified:

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

Now, we compare the simplified arithmetic sequence formula \( a_n = 8n - 2 \) with the provided linear function options:

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

We can see that the first option, \( y = 8x - 2 \), matches the structure of our simplified arithmetic sequence \( a_n = 8n - 2 \).

Thus, the correct response is:

y = 8x - 2