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Writing and Using Explicit Rules for Arithmetic Sequences

Writing and Using Explicit Rules for Arithmetic Sequences 1.1 - Solution

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To begin, let's observe the given terms in the sequence to determine the value of the first term as well as the common difference. We can use this information to write an equation for the term of the sequence.

Writing the Equation

Explicit equations for the term of an arithmetic sequence follow a certain format. In this form, is the first term in the sequence, is the common difference, and is the position of the desired term in the sequence. Using the common difference and the first term , we can write and simplify the equation.
We can calculate the fifth term of the sequence, , by substituting into our equation.
The fifth term is

Graphing the Sequence

When graphing a sequence, the axis always represents the number of the term and the axis represents the value of the term

Now let's graph these points on a coordinate plane.