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=6x+8
y equals 6 x plus 8

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

y=8x−2

Answer 1

To analyze the arithmetic sequence given by the formula \( a_n = 6 + (n - 1) \cdot 8 \), we can first rewrite it in a more standard form:

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

This shows that the arithmetic sequence can be expressed in the form of a linear function where it has the structure \( y = mx + b \) with \( m = 8 \) and \( b = -2 \).

Now, looking at the provided options:

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

The correct choice that matches the structure of the arithmetic sequence \( a_n = 8n - 2 \) is:

\( y = 8x - 2 \)

So, the answer is \( y = 8x - 2 \).