Question

A) 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. (1 point)
y = 6x + 8
y = 2x − 8
y = 8x − 2
y = 8x + 6

Answer 1

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

Starting with the given formula:

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

Distributing the \( 8 \):

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

Combining like terms:

\[
a_n = 8n - 2
\]

Now we can compare this with the general form of a linear function, which is \( y = mx + b \). In this context, \( a_n \) corresponds to \( y \), \( n \) corresponds to \( x \), \( 8 \) corresponds to the slope \( m \), and \( -2 \) corresponds to the y-intercept \( b \).

Now, looking at the given options:

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

The only function that matches our derived formula \( a_n = 8n - 2 \) is:

\[
y = 8x - 2
\]

Thus, the correct answer is:

**y = 8x - 2.**