Find the

twentiethtwentieth

term of the arithmetic sequence whose first term is

6

and whose common difference is

negative −2.

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Part 1

a 20a20equals=enter your response here

To find the 20th term (\(a_{20}\)) of an arithmetic sequence, we use the formula:

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

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term position.

### Given:
- \(a_1 = 6\),
- \(d = -2\),
- \(n = 20\).

Substitute into the formula:

\[
a_{20} = 6 + (20 - 1) \cdot (-2)
\]
\[
a_{20} = 6 + 19 \cdot (-2)
\]
\[
a_{20} = 6 - 38
\]
\[
a_{20} = -32
\]

### Final Answer:
\[
a_{20} = -32
\]

Would you like more details or have any questions? Here are 5 related questions to explore further:

1. How do you determine the general term formula for any arithmetic sequence?
2. What happens to the terms of an arithmetic sequence when the common difference is negative?
3. Can you derive the sum of the first 20 terms of this sequence?
4. How would the 20th term change if the common difference were positive?
5. What are some real-world applications of arithmetic sequences?

**Tip**: Always double-check the signs of the common difference and ensure proper substitution into formulas to avoid errors.

Find the twentieth term of the arithmetic sequence whose first term is 6 and whose common difference is −2.

Explore how to find the 20th term of an arithmetic sequence where the first term is 6 and the common difference is -2. This step-by-step solution uses the general term formula for arithmetic sequences and applies key algebraic concepts. Suitable for Grades 8-10.

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