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=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 show that the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \) has the same structure as a linear function, let's rewrite the sequence formula in a more recognizable linear form.

Starting from the given arithmetic sequence:

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

Distributing the 8 gives:

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

This simplifies to:

\[ a_n = 8n - 2 \]

Now, we can see that the arithmetic sequence \( a_n \) is structured as a linear function of the form \( y = mx + b \), where \( m \) is the coefficient of \( n \) (which corresponds to the slope), and \( b \) is the y-intercept.

Comparing this with the provided options, the equivalent linear function is:

\[ y = 8x - 2 \]

Thus, the correct choice is:

y = 8x - 2.