Question

page 17 of 17
Arithmetic Sequences Quick Check
3 of 53 of 5 Items
Question
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
.(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 \( a_n = 6 + (n - 1) \cdot 8 \) can be related to a linear function, we can first simplify the given formula:

1. Distribute the 8:
\( a_n = 6 + 8n - 8 \)
\( a_n = 8n - 2 \)

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

From our simplification, we see that:
- The slope \( m \) is 8.
- The y-intercept \( b \) is -2.

Thus, the equation \( a_n \) can be written as:
\( a_n = 8n - 2 \)

Now, we can compare this to the response options provided. The correct answer is:

**y = 8x - 2**

This is the linear function that matches the structure of the given arithmetic sequence formula.