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What is the next number in the sequence: 3, 7, 15, 31, 63?

  1. 94

  2. 126

  3. 137

  4. 127

The correct answer is: 127

To identify the next number in the sequence, observe the pattern in the differences between consecutive numbers. Starting with the provided sequence: - The difference between 3 and 7 is 4. - The difference between 7 and 15 is 8. - The difference between 15 and 31 is 16. - The difference between 31 and 63 is 32. The differences themselves form a sequence: 4, 8, 16, 32. These differences are doubling each time (4 × 2 = 8, 8 × 2 = 16, 16 × 2 = 32). Following this pattern, the next difference should be 32 × 2, which equals 64. Adding this difference to the last number in the original sequence, we have: 63 + 64 = 127. Thus, 127 is the next number in the sequence. The process of identifying the geometric growth in the differences between the numbers leads us directly to this conclusion, reaffirming that the answer is indeed correct in the context of the sequence progression.