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=8x+6
y equals 8 x plus 6

y=2x−8
y equals 2 x minus 8

y=6x+8

Answer 1

To determine which linear function has the same structure as the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \), let's rewrite the arithmetic sequence formula in a standard linear function form, \( y = mx + b \).

The formula for the arithmetic sequence can be simplified:

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

Distributing the 8 gives:

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

Combining the constant terms yields:

\[ a_n = 8n - 2 \]

This has the form \( y = mx + b \) where \( m = 8 \) and \( b = -2 \).

Now, looking at your options:

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

The correct response that matches the structure of the arithmetic sequence formula is:

y = 8x - 2.