The given series is an arithmetic sequence where each term decreases by a constant value.

**First term (\(a_1\))**: \(3\)  
**Common difference (\(d\))**: \(1 - 3 = -2\)

To find the \(n\)th term of the sequence, use the formula:

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

Given that \(a_n = -27\), substitute the known values:

\[
-27 = 3 + (n - 1) \times (-2)
\]

Now, solve for \(n\):

1. Subtract 3 from both sides:

\[
-27 - 3 = (n - 1) \times (-2)
\]

\[
-30 = (n - 1) \times (-2)
\]

2. Divide both sides by \(-2\):

\[
n - 1 = \frac{-30}{-2} = 15
\]

3. Add 1 to both sides:

\[
n = 15 + 1 = 16
\]

So, the term \(-27\) is the **16th term** in the series.

Would you like further details on this calculation or any other related questions?

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Here are 5 related questions:
1. What is the sum of the first 16 terms of this arithmetic sequence?
2. How would you find the 10th term in the same sequence?
3. What happens to the sequence if the common difference is changed?
4. Can you find the middle term in a sequence with an odd number of terms?
5. How would you find the first term if only the 16th term and common difference were known?

**Tip:** Arithmetic sequences are linear, meaning that the difference between consecutive terms remains constant, which makes them predictable and easy to analyze.

Learn how to find the -27th term in the arithmetic sequence 3, 1, -1 using the arithmetic sequence nth term formula. This problem involves calculating the position of a term in a sequence with a constant difference between terms. Suitable for high school students.

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