AP Precalculus Practice Test: Unit 2 Question #1 Find the nth Term of an Arithmetic Sequence

My AP Precalculus Practice Tests are carefully designed to help students build confidence for in-class assessments, support their work on AP Classroom assignments, and thoroughly prepare them for the AP Precalculus exam in May.

To find the \( n \)-th term of an arithmetic sequence, we use the formula:

\[
a_n = a_1 + (n-1)d
\]

where:
- \( a_n \) is the \( n \)-th term.
- \( a_1 \) is the first term of the sequence.
- \( d \) is the common difference (the amount added to each term to get the next term).
- \( n \) is the position of the term you’re finding.

### Example:
**Question:** The first term of an arithmetic sequence is \( a_1 = 5 \), and the common difference is \( d = 3 \). Find the 10th term (\( a_{10} \)).

**Solution:**
\[
a_{10} = a_1 + (10-1)d
\]
\[
a_{10} = 5 + 9(3)
\]
\[
a_{10} = 5 + 27 = 32
\]

So, the 10th term is **32**.

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For your AP Precalculus Unit 2 Practice Test:
The question likely provides values for \( a_1 \), \( d \), and \( n \), or it asks you to determine \( d \) from consecutive terms before finding the \( n \)-th term. Make sure to:
1. Identify \( a_1 \), \( d \), and \( n \) from the given information.
2. Substitute them into the formula.
3. Simplify to find \( a_n \).

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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