Question

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**.