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Write the first few terms of the sequence.
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on
The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.
In function notation, the sequence is
This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5.
A graph of the line is shown below.
Answer:
The sequence is
The slope is 5.
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on
The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.
In function notation, the sequence is
This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5.
A graph of the line is shown below.
Answer:
The sequence is
The slope is 5.
There are two ways to approach this.
Option #1:
Use the slope formula .
That value is undefined, so the slope is undefined.
Option #2:
Because the two points have the same x-value, they will be vertically above/below one another. This means your line is a vertical line and the slope of a vertical line is undefined.
Either way, your slope is undefined.