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

To determine the 10th term in the given sequence \(0, 1, 2, 9, 8, \ldots\), we need to first identify the pattern or rule governing the sequence.

Observing the terms provided:

1. \(a_1 = 0\)
2. \(a_2 = 1\)
3. \(a_3 = 2\)
4. \(a_4 = 9\)
5. \(a_5 = 8\)

One possible way to approach this is to look for a repeating pattern or transformation. Given the first few terms, let's see if there is a pattern for the first few terms:

- The first three terms are \(0, 1, 2\), which appear to be simple increments.
- The fourth and fifth terms are \(9, 8\), which might suggest a decrement from 9.

Now, checking if there’s any periodic pattern, consider the terms modulo 10:
- \(0, 1, 2, 9, 8\)

Let's assume the sequence has a period of 5. This implies that every 5 terms, the sequence repeats itself. To determine the 10th term, we consider:

\[10 \mod 5 = 0\]

Since the 10th term is at a position that is a multiple of 5, it corresponds to the last position of one complete period (which is 5). So,

Learn how to find the 10th term in the sequence 0, 1, 2, 9, 8 using mathematical analysis. This sequence involves exploring patterns and applying modulo arithmetic to determine the correct term. Suitable for students in Grades 7-9.

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