Arithmetic Sequences Quick Check

Question

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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=8x−2
y equals 8 x minus 2

y=2x−8
y equals 2 x minus 8

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

y=6x+8

Answer 1

To identify which linear function has the same structure as the arithmetic sequence \( a_n = 6 + (n - 1) \cdot 8 \), we can start by rewriting the arithmetic sequence formula in slope-intercept form (which is the standard form of a linear function, \( y = mx + b \)).

The given formula for the arithmetic sequence can be simplified:

1. Distribute the \( 8 \): \[ a_n = 6 + (n - 1) \cdot 8 = 6 + 8n - 8 \]
2. Combine like terms: \[ a_n = 8n - 2 \]

Now, set \( a_n \) equal to \( y \) and \( n \) equal to \( x \) to align it with the form \( y = mx + b \): \[ y = 8x - 2 \]

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

• y = 8x - 2.