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=8x−2
y equals 8 x minus 2

y=6x+8
y equals 6 x plus 8

y=8x+6
y equals 8 x plus 6

y=2x−8

Answer 1

To compare the arithmetic sequence formula \( a_n = 6 + (n-1) \cdot 8 \) with a linear function, we can rewrite the arithmetic sequence in a more familiar form.

Start with the given formula:

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

Distributing the \( 8 \):

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

Combining the constants:

\[ a_n = 8n - 2 \]

Now, we can see that this resembles the structure of a linear function in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Comparing this with the given options:

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

The correct choice that matches the structure of the arithmetic sequence formula \( a_n \) is:

\[ y = 8x - 2 \]

So the answer is:

y = 8x - 2