Multiple choice

Complete the series given below by choosing the missing term from the given alternatives. $5, 9, 16, 29, 54, ?$

  1. $103$
  2. $105$
  3. $109$

  4. None of these
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A Correct answer
Explanation

The pattern is: 5 + 4 = 9; 9 + 7 = 16; 16 + 13 = 29; 29 + 25 = 54. The differences are 4, 7, 13, 25. These follow the pattern (diff * 2 - 1): 4*2-1=7, 7*2-1=13, 13*2-1=25, 25*2-1=49. 54 + 49 = 103.

AI explanation

The differences between the terms are 4, 7, 13, and 25, and the second differences of these numbers are 3, 6, and 12, which doubles each time. Following this doubling pattern, the next second difference is 24, making the next first difference 25 + 24 = 49. Adding 49 to 54 gives the missing term as 103.

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