The 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. The Following are the provided options y=8x+6, y=8x-2, y=6x+2, y=2x-8.

Answer 1

To show that the arithmetic sequence formula has the same structure as a linear function, we can start with the given arithmetic sequence formula:

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

We can simplify that expression.

First, distribute the \(8\):

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

Now, simplify it:

\[ a_n = 8n - 2 \]

This is now in the form of the linear function \(y = mx + b\) where \(m\) (the slope) is 8 and \(b\) (the y-intercept) is -2. Therefore, the correct linear function that has the same structure as the arithmetic sequence is:

\[ y = 8x - 2 \]

So, the choice from the provided options is:

y = 8x - 2.