Question

points for finding hidden door
how is the slope of the line related to the arithmetic sequence?
it is the first term.
it is the common difference.
it is the last term.

Explanation:

Identify the sequence terms

Using the Arithmetic Sequences knowledge point
The points plotted on the graph represent the terms of an arithmetic sequence where the level \(x\) is the term number and the points \(y\) are the term values:

• Term 1: \(50\)
• Term 2: \(200\)
• Term 3: \(350\)
• Term 4: \(500\)
• Term 5: \(650\)

Relate slope to common difference

Using the Slope Formula and Arithmetic Sequences knowledge points

$$ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{200 - 50}{2 - 1} = 150 $$

In an arithmetic sequence, the constant rate of change between consecutive terms is the common difference \(d\):

$$ d = a_n - a_{n-1} = 200 - 50 = 150 $$

Thus, the slope of the line is equal to the common difference of the arithmetic sequence.

Answer:

• It is the first term.
• It is the common difference. (Correct answer)
• It is the last term.