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The sequence provided is \(-2, -5, -8, -11, -14, \dots\). This is an arithmetic sequence where the common difference \(d\) between consecutive terms can be determined as:

\[
d = -5 - (-2) = -3
\]

The first term \(a_1\) is \(-2\). The formula for the \(n\)-th term of an arithmetic sequence is:

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

We are tasked with finding the 22nd term (\(a_{22}\)):

\[
a_{22} = -2 + (22 - 1) \cdot (-3)
\]
\[
a_{22} = -2 + 21 \cdot (-3)
\]
\[
a_{22} = -2 - 63
\]
\[
a_{22} = -65
\]

Therefore, the 22nd term is \(-65\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do we derive the general formula for any arithmetic sequence?
2. Can we find the sum of the first 22 terms in this sequence?
3. What happens if the common difference was positive, how would the sequence change?
4. How would you determine the number of terms if a specific value is known in the sequence?
5. How does this formula apply if the sequence was geometric instead of arithmetic?

**Tip:** Always identify the common difference in an arithmetic sequence before proceeding to solve for any specific term.

Find the 22nd term of the sequence: -2, -5, -8, -11, -14, ...

Learn how to find the 22nd term of the arithmetic sequence: -2, -5, -8, -11, -14, ... This solution demonstrates the use of the arithmetic sequence formula and identifies the common difference. Suitable for students in Grades 7-9.

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