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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.The sequence is . We need to determine if there is a common ratio or difference that can help us find the missing number.
- Check Geometric Sequence: Check if the sequence is geometric.To determine if the sequence is geometric, we can divide consecutive terms (where possible) to find a common ratio. We have:Both the ratios are equal to , which suggests that the sequence might be geometric with a common ratio of .
- Confirm Common Ratio: Confirm the common ratio for the entire sequence.We need to confirm that the common ratio of applies to the first two terms as well. However, since the second term is and the first term is , dividing by gives us , which is consistent with our common ratio. This confirms that the sequence is indeed geometric with a common ratio of .
- Calculate Missing Number: Calculate the missing number using the common ratio.Since the sequence is geometric with a common ratio of , we can find the missing number by multiplying the first term by the common ratio twice (since the missing number is the third term in the sequence). Therefore:The missing number in the sequence is .
