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−2
y equals 8 x minus 2

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

y=2x−8
y equals 2 x minus 8

y=6x+8

Answer 1

To find the linear function that has the same structure as the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \), we can rewrite the arithmetic sequence formula in a form that resembles a linear equation.

The formula for the arithmetic sequence can be expanded as follows:

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

Now, we have the form \( a_n = 8n - 2 \).

This matches the structure of the linear function \( y = mx + b \), where \( m \) is the coefficient of \( n \) and \( b \) is a constant.

So, the equivalent linear function with the same structure is:

\[ y = 8x - 2 \]

Therefore, the correct response is:

y = 8x - 2.