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Type the missing number in this sequence:, , , , , ,
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Q. Type the missing number in this sequence:, , , , , ,
- Identify Pattern: Identify the pattern in the sequence.We notice that the sequence is not immediately recognizable as an arithmetic or geometric sequence. We need to look at the differences between the numbers to see if there is a pattern.
- Calculate Differences: Calculate the differences between the numbers.The difference between and is .The difference between and is .The difference between and is .The difference between and is .The difference between and is .
- Analyze Differences: Analyze the differences for a pattern.The differences do not form a simple arithmetic sequence. However, we can notice that the differences between the differences are consistent: , , . This suggests that the differences themselves may be increasing by a constant amount.
- Determine Pattern: Determine the pattern of the differences.If we assume the differences increase by a constant amount, we can try to find the missing difference. Since the difference between and is , and the difference between and is , we can infer that the difference before should be . Therefore, the missing number should be .
- Verify Pattern: Verify the pattern with the next number in the sequence.If the missing number is indeed , then the difference between and should be , which fits our pattern of increasing differences (, ). The next difference is (), and then (), and finally (). This confirms our pattern.
