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

Question

.(1 point)
Responses

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

y=2x−8
y equals 2 x minus 8

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

y=8x−2
y equals 8 x minus 2

Answer 1

To find 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 rewrite the formula in a more familiar linear form.

The given arithmetic sequence can be simplified:

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

Now, the equation is in the form \( a_n = 8n - 2 \).

To compare it with the typical linear function form, we can identify \( y = 8x - 2 \). Here, \( a_n \) is analogous to \( y \) and \( n \) is analogous to \( x \).

Looking at the provided responses, the correct linear function that matches the structure of the arithmetic sequence \( a_n = 6 + (n - 1) \cdot 8 \) is:

y = 8x - 2.