3. If a1 = –17 and d = 4, find 
a22 of the arithmetic 
sequence

To find the 22nd term (\(a_{22}\)) of the arithmetic sequence, you can use the formula for the nth term of an arithmetic sequence:

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

Given:
- \(a_1 = -17\) (the first term),
- \(d = 4\) (the common difference),
- \(n = 22\) (the term number you want to find).

Substitute these values into the formula:

\[
a_{22} = -17 + (22 - 1) \times 4
\]

Simplifying:

\[
a_{22} = -17 + 21 \times 4
\]

\[
a_{22} = -17 + 84
\]

\[
a_{22} = 67
\]

Thus, the 22nd term of the arithmetic sequence is \(a_{22} = 67\).

Would you like more details or have any questions?

Here are some related questions:
1. How would you calculate the 100th term of this sequence?
2. What is the sum of the first 22 terms of this sequence?
3. How can you determine the common difference \(d\) if only two terms are given?
4. What would happen to the sequence if the common difference \(d\) were negative?
5. How do you find the first term if the 22nd term and common difference are known?
6. What is the formula for the sum of an arithmetic sequence?
7. Can an arithmetic sequence have a common difference of zero? What would it look like?
8. How does changing the first term affect the entire sequence?

**Tip:** When solving problems involving sequences, always double-check which term number \(n\) you need to find to avoid errors.

Learn how to find the 22nd term (a22) of an arithmetic sequence with the first term (a1) of -17 and a common difference (d) of 4. Follow the step-by-step solution using the arithmetic sequence nth term formula. Suitable for students in Grades 7-9.

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