Multiple choice

Find the missing term and complete the sequence. 163, 134, 111, 94, 83, ?

  1. 57

  2. 60

  3. 69

  4. 78

  5. None of these
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D Correct answer
Explanation

Differences: 163-134=29, 134-111=23, 111-94=17, 94-83=11. The differences are primes in descending order (29, 23, 17, 11, 5). 83 - 5 = 78.

AI explanation

The differences between the terms are the cubes of consecutive odd numbers subtracted from the previous term. The differences are 163 - 134 = 29, 134 - 111 = 23, 111 - 94 = 17, and 94 - 83 = 11, which are the cubes of 3, 3, 3, and 3 respectively, minus decreasing multiples. Noticing the second differences are all 6, the next difference is 11 - 6 = 5. Subtracting 5 from 83 gives the missing term 78.

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