Question

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 a^n=6+(n−1)⋅8

y=2x-8
y=6x+8
y=8x+6
y=8x-2

Answer 1

To show that the arithmetic sequence formulas have the same structure as linear functions, we start with the arithmetic sequence formula given:

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

We can rewrite this formula to identify its structure as a linear function.

First, expand the equation:

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

So, we can express it as:

\[
a^n = 8n - 2
\]

This equation is in the form of \(y = mx + b\), where \(m = 8\) and \(b = -2\).

Now, let's compare this with the provided linear function options:

1. \(y = 2x - 8\)
2. \(y = 6x + 8\)
3. \(y = 8x + 6\)
4. \(y = 8x - 2\)

The linear function that has the same structure as the arithmetic sequence \(a^n = 8n - 2\) is:

\[
y = 8x - 2
\]

Thus, the correct answer is:

\[
\boxed{y = 8x - 2}
\]