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=2x−8
y equals 2 x minus 8

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

y=8x−2
y equals 8 x minus 2

y=6x+8

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 rearrange the formula into the form \( a_n = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting from the given formula:

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

We can distribute the 8:

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

Now, simplify it:

\[ a_n = 8n - 2 \]

This shows that the arithmetic sequence can be expressed in the form of a linear function where \( m = 8 \) (the coefficient of \( n \), or the slope) and \( b = -2 \) (the constant term).

Now, we need to find the linear function equation that matches this structure, specifically:

\[ y = 8x - 2 \]

So the correct response is:

y = 8x - 2