To find the missing number in the sequence 3, 12, 48, 192, ____, 3,072, we can look at how each term relates to the ones before it.
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From 3 to 12: \( 12 = 3 \times 4 \)
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From 12 to 48: \( 48 = 12 \times 4 \)
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From 48 to 192: \( 192 = 48 \times 4 \)
It appears that each number is being multiplied by 4 to get the next number in the sequence.
Following this pattern, we can find the next number:
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From 192 to the missing number: \( \text{Missing number} = 192 \times 4 = 768 \)
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Now we can check the next step to confirm: \( 768 \times 4 = 3,072 \)
Everything matches up, so the missing number in the sequence is:
768