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Writing and Using Explicit Rules for Arithmetic Sequences

Writing and Using Explicit Rules for Arithmetic Sequences 1.4 - Solution

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a

Using the graph, we can list the first five terms of the sequence. Notice that the -axis shows us the term number. The -axis show us the value of the terms.

b
Let's use the formula for the term of an arithmetic sequence to write an equation for the sequence. In this equation, is a first term and is the common difference. From Part A, we know that the first term is To find we can calculate the difference between any two consecutive terms. Here we will use the fourth and fifth terms. Now we can substitute these values into the formula.
The formula for the th term is
c
To write the function we can use the slope-intercept form of the equation. We can take two points from the graph and substitute them into the Slope Formula. Let's use and
Simplify
Let's now calculate by substituting and the point into the equation.
Simplify
Now that we know both and we can write the function.