3. If a1 = –17 and d = 4, find3. If a1 = –17 and d = 4, find 

a22 of the arithmetic 

sequence
a22 of the arithmetic%
sequence

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

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

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

Now, substitute the given values into the formula:

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

Simplify the expression:

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

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

\[
a_{22} = 67
\]

So, 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. What is the general formula for the nth term in an arithmetic sequence?
2. How do you find the sum of the first n terms in an arithmetic sequence?
3. How do you determine if a sequence is arithmetic?
4. What happens if the common difference \(d\) is negative?
5. How can you find the common difference if you're given two non-consecutive terms?
6. What is the 50th term of the same arithmetic sequence?
7. How do you solve for \(n\) when given \(a_n\), \(a_1\), and \(d\)?
8. How do you derive the formula for the nth term in an arithmetic sequence?

**Tip:** In an arithmetic sequence, if you know the first term and the common difference, you can easily find any term using the formula for the nth term.

Learn how to find the 22nd term of an arithmetic sequence where the first term is -17 and the common difference is 4. Step-by-step solution provided with the formula for the nth term of an arithmetic sequence.

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