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+(nā1)ā
8
.(1 point)
Responses
y=2xā8
y equals 2 x minus 8
y=8x+6
y equals 8 x plus 6
y=8xā2
y equals 8 x minus 2
y=6x+8
.(1 point)
Responses
y=2xā8
y equals 2 x minus 8
y=8x+6
y equals 8 x plus 6
y=8xā2
y equals 8 x minus 2
y=6x+8
Answers
GPT-4o mini
To show that the arithmetic sequence formula \( a_n = 6 + (n - 1) \cdot 8 \) has the same structure as a linear function, we can rearrange the formula into the form \( a_n = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting from the given formula:
\[
a_n = 6 + (n - 1) \cdot 8
\]
We can distribute the 8:
\[
a_n = 6 + 8n - 8
\]
Now, simplify it:
\[
a_n = 8n - 2
\]
This shows that the arithmetic sequence can be expressed in the form of a linear function where \( m = 8 \) (the coefficient of \( n \), or the slope) and \( b = -2 \) (the constant term).
Now, we need to find the linear function equation that matches this structure, specifically:
\[
y = 8x - 2
\]
So the correct response is:
**y = 8x - 2**
Starting from the given formula:
\[
a_n = 6 + (n - 1) \cdot 8
\]
We can distribute the 8:
\[
a_n = 6 + 8n - 8
\]
Now, simplify it:
\[
a_n = 8n - 2
\]
This shows that the arithmetic sequence can be expressed in the form of a linear function where \( m = 8 \) (the coefficient of \( n \), or the slope) and \( b = -2 \) (the constant term).
Now, we need to find the linear function equation that matches this structure, specifically:
\[
y = 8x - 2
\]
So the correct response is:
**y = 8x - 2**
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