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=2x−8
y equals 2 x minus 8

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

y=8x+6

Answer 1

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

The formula for the \( n \)-th term of the arithmetic sequence can be simplified as follows:

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

Now, we have represented the arithmetic sequence in a linear form \( a_n = 8n - 2 \).

The corresponding linear function in the responses can be identified as:

\[ y = 8x - 2 \]

Thus, the linear function that has the same structure as the arithmetic sequence is:

y = 8x - 2.