What is the pattern behind the series 2, 4, 8, 16, 32?

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The series 2, 4, 8, 16, 32 is a sequence of numbers where each term is obtained by multiplying the previous term by 2. This is known as a geometric progression, and in this case, the first term (a) is 2, and the common ratio (r) is also 2.

Let’s break it down:

  • The first term is 2.
  • The second term is 2 × 2 = 4.
  • The third term is 4 × 2 = 8.
  • The fourth term is 8 × 2 = 16.
  • The fifth term is 16 × 2 = 32.

To generalize the pattern of this series, you can express the nth term using the formula:

    a_n = a × r^(n-1)

In this case:

    a_n = 2 × 2^(n-1)

For example:

  • If n = 1, then a_1 = 2 × 2^(1-1) = 2.
  • If n = 2, then a_2 = 2 × 2^(2-1) = 4.
  • If n = 3, then a_3 = 2 × 2^(3-1) = 8.
  • If n = 4, then a_4 = 2 × 2^(4-1) = 16.
  • If n = 5, then a_5 = 2 × 2^(5-1) = 32.

This series continues indefinitely, and the next term would be 32 × 2 = 64. Thus, we can conclude that the series represents the powers of 2 starting from 21 up to 25.

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