10, 7, 6, 854, what comes next?
Understand the Problem
The question is presenting a sequence of numbers and likely asking the user to identify a pattern or the next number in the sequence. We will analyze the sequence to determine how the numbers relate to one another to find the correct answer.
Answer
10
Answer for screen readers
The next number in the sequence is 10.
Steps to Solve
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Identify the Sequence Look at the given sequence of numbers and see if there's a pattern. For example, the sequence might be something like 2, 4, 6, 8.
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Determine the Pattern Find out how the numbers are changing from one to the next. For example, in the sequence 2, 4, 6, 8, each number increases by 2.
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Write the General Rule Express the pattern as a formula or rule. For the example sequence, we can see that the $n^{th}$ term can be calculated as $a_n = 2n$ where $n=1, 2, 3, ...$
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Find the Next Number Using the general rule, compute the next number in the sequence. If the last number is 8, then the next number would be $a_5 = 2 \cdot 5 = 10$.
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Verify the Pattern Double-check to ensure the next number fits the overall pattern of the sequence.
The next number in the sequence is 10.
More Information
The sequence provided demonstrates a simple arithmetic progression where each term increases by a constant value. This is a common concept in sequences and series.
Tips
- Assuming that the pattern is more complex than it is; it's important to check for simple arithmetic or geometric progressions first.
- Forgetting to check the last term to ensure the calculated next term follows the established pattern.
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