A sequence is in the form 0,1,2,9,8. The 10th term in the sequence is

A 510

The sequence given is \( 0, 1, 2, 9, 8 \). To find the 10th term, let's look for a pattern or formula.

First, observe the terms:
- The 1st, 2nd, and 3rd terms are \( 0, 1, 2 \).
- The 4th and 5th terms are \( 9 \) and \( 8 \).

There appears to be two different patterns: the first three terms increase by 1, and the next two terms are 9 and 8. The key is to determine if this pattern repeats.

To determine the pattern, consider checking:
1. If the sequence repeats every 5 terms.
2. If the sequence involves simple arithmetic progressions or other operations.

Given the sequence 0, 1, 2, 9, 8:
- 1st term (0)
- 2nd term (1)
- 3rd term (2)
- 4th term (9)
- 5th term (8)

If the sequence repeats every 5 terms, the 10th term would be the same as the 5th term.

To verify, calculate \( 10 \div 5 = 2 \), remainder 0, indicating the sequence completes exactly two full cycles by the 10th term. Thus, the 10th term is the same as the 5th term.

**Conclusion:** The 10th term of the sequence is \( 8 \).

Would you like a detailed explanation or have any questions?

Here are some related questions:
1. What is the general term formula for this sequence?
2. How does identifying the repeating pattern help in sequences?
3. Can this sequence be represented as a function?
4. What are the properties of arithmetic and geometric sequences?
5. How can one determine if a sequence is arithmetic or geometric?
6. What other types of sequences exist in mathematics?
7. How do you find the sum of the first \( n \) terms in a sequence?
8. How does understanding sequences apply to real-world situations?

**Tip:** When identifying patterns in sequences, consider if the pattern could be arithmetic, geometric, or follow another recognizable rule. This can simplify finding terms further along in the sequence.

Discover how to find the 10th term in the sequence 0, 1, 2, 9, 8 with a step-by-step explanation. This problem involves recognizing patterns in sequences, particularly arithmetic sequences, and determining the term based on identified patterns. Suitable for students in Grades 7-9.

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