Find the 17th term of the arithmetic sequence of -13,-8,-3,2

In an arithmetic sequence, each term increases by a constant difference. The general formula for the \(n\)-th term of an arithmetic sequence is:

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

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the position of the term.

### Step 1: Identify the first term \(a_1\) and the common difference \(d\)
- \(a_1 = -13\)
- To find the common difference \(d\), subtract the first term from the second term:
  \[
  d = -8 - (-13) = 5
  \]

### Step 2: Plug values into the formula to find the 17th term \(a_{17}\)
\[
a_{17} = -13 + (17 - 1) \cdot 5
\]
\[
a_{17} = -13 + 16 \cdot 5
\]
\[
a_{17} = -13 + 80 = 67
\]

The 17th term of the arithmetic sequence is **67**.

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What is the formula for the sum of the first \(n\) terms of an arithmetic sequence?
2. How would you find the 50th term of this arithmetic sequence?
3. Can you calculate the common difference if only the first and last terms of an arithmetic sequence are known?
4. How do you identify an arithmetic sequence from a set of numbers?
5. What are the properties of arithmetic sequences compared to geometric sequences?

**Tip:** In arithmetic sequences, knowing the common difference allows you to predict any term in the sequence quickly.

Learn how to find the 17th term of the arithmetic sequence -13, -8, -3, 2 using the nth-term formula. Understand the concept of arithmetic sequences and the formula to predict any term in the sequence. Suitable for students in Grades 7-9.

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