Let's observe the given sequence step by step: [tex]\(8, 1, 7, 0, 6, -1, \ldots\)[/tex].
1. First, separate the terms based on their positions:
- Terms at odd positions: [tex]\(8, 7, 6, \ldots\)[/tex]
- Terms at even positions: [tex]\(1, 0, -1, \ldots\)[/tex]
2. Analyze the sequence for terms at odd positions:
[tex]\[
8 \rightarrow 7 \rightarrow 6
\][/tex]
- Here, each term is decreasing by 1. Continuing this pattern, the next term after 6 would be [tex]\(6 - 1 = 5\)[/tex].
3. Now, inspect the sequence for terms at even positions:
[tex]\[
1 \rightarrow 0 \rightarrow -1
\][/tex]
- Similarly, each term is decreasing by 1. Continuing this pattern, the next term after -1 would be [tex]\(-1 - 1 = -2\)[/tex].
4. According to the sequence pattern, the term [tex]\(6, -1\)[/tex] are in the 5th and 6th positions respectively. The 7th term would be the next term in the even position sequence since the positions alternate (odd, even).
Therefore, the next term in the sequence is [tex]\(-2\)[/tex].
