What is the next number in the series 1, 4, 9, 16?

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The sequence you’ve provided is comprised of the first four square numbers. Let’s break it down:

  1. The first term is 1 (which is 1 squared, or 12).
  2. The second term is 4 (which is 2 squared, or 22).
  3. The third term is 9 (which is 3 squared, or 32).
  4. The fourth term is 16 (which is 4 squared, or 42).

Following this pattern, it’s clear that the series is simply the squares of the integers in order:

  • 12 = 1
  • 22 = 4
  • 32 = 9
  • 42 = 16
  • 52 = 25

Hence, the number that should come next in the series is 25.

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