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The given sequence is defined as:

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

We are tasked with finding the 20th term of this sequence, i.e., \( a_{20} \).

Let's substitute \( n = 20 \) into the formula:

\[
a_{20} = (20 - 1)(2 - 20)(3 + 20)
\]

Simplifying each part:

\[
a_{20} = (19)(2 - 20)(3 + 20)
= 19 \times (-18) \times 23
\]

Now, let's multiply step by step:

\[
19 \times (-18) = -342
\]

\[
-342 \times 23 = -7866
\]

Therefore, the 20th term of the sequence is \( a_{20} = -7866 \).

The correct option is:

**C. -7866**

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Would you like further details or explanations? Here are five related questions you could explore:

1. How do we find the general term of a sequence given a different formula?
2. Can you explain how sequences are classified (arithmetic, geometric, etc.)?
3. What happens to the terms of the sequence as \( n \) increases? Does the behavior follow any pattern?
4. How do we determine if a sequence is convergent or divergent?
5. How can this sequence be visualized on a graph?

**Tip:** Always break down complex calculations into smaller steps to avoid mistakes.

What is the 20th term of the sequence defined by an = (n - 1)(2 - n)(3 + n)?

Learn how to calculate the 20th term of a sequence defined by an = (n - 1)(2 - n)(3 + n). This detailed solution breaks down the step-by-step process of simplifying the sequence formula, making it suitable for high school students. Ideal for Grades 9-12.

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