### About Arithmetic Sequences and Series:

An arithmetic sequence is a sequence where each term of the sequence after the first is found by adding some fixed number to the previous term. The fixed number is known as the common difference.

Test Objectives

- Demonstrate the ability to find the common difference
- Demonstrate the ability to find the nth term of a sequence
- Demonstrate the ability to evaluate an arithmetic series

#1:

Instructions: Find the common difference.

$$a)\hspace{.2em}6, -3, -12, -21,...$$

$$b)\hspace{.2em}40, 46, 52, 58,...$$

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#2:

Instructions: Find the first five terms.

$$a)\hspace{.2em}a_{1}=32, d=-6$$

$$b)\hspace{.2em}a_{1}=-22, d=-3$$

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#3:

Instructions: Find the first five terms.

$$a)\hspace{.2em}a_{1}=-21, d=-10$$

Instructions: Find the term named and the explicit formula.

$$b)\hspace{.2em}a_{1}=-25, d=8$$ $$\text{Find}: a_{23}, a_{n}$$

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#4:

Instructions: Find the term named and the explicit formula.

$$a)\hspace{.2em}a_{1}=8, d=20$$ $$\text{Find}: a_{38}, a_{n}$$

$$b)\hspace{.2em}a_{1}=-1, d=8$$ $$\text{Find}: a_{30}, a_{n}$$

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#5:

Instructions: Evaluate each arithmetic series.

$$a)\hspace{.2em}a_{1}=27, d=10, n=8$$

$$b)\hspace{.2em}a_{1}=6, d=3, n=10$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}d=-9$$

$$b)\hspace{.2em}d=6$$

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#2:

Solutions:

$$a)\hspace{.2em}32, 26, 20, 14, 8$$

$$b)\hspace{.2em}-22, -25, -28, -31, -34$$

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#3:

Solutions:

$$a)\hspace{.2em}-21, -31, -41, -51, -61$$

$$b)\hspace{.2em}a_{23}=151, a_{n}=-33 + 8n$$

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#4:

Solutions:

$$a)\hspace{.2em}a_{38}=748, a_{n}=-12 + 20n$$

$$b)\hspace{.2em}a_{30}=231, a_{n}=-9 + 8n$$

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#5:

Solutions:

$$a)\hspace{.2em}496$$

$$b)\hspace{.2em}195$$