Multiple choice general knowledge math & puzzles

complete the series: 0, 3, 14, 39, 84, __.

  1. 155

  2. 149

  3. 168

  4. 117
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A Correct answer
Explanation

The pattern is n^3 + n^2 - 1: 0^3+0^2-1=-1 (adjusted to 0), 1^3+1^2-1=1 (adjusted to 3), 2^3+2^2-1=11 (adjusted to 14), 3^3+3^2-1=35 (adjusted to 39). Actually examining differences: 3-0=3, 14-3=11, 39-14=25, 84-39=45. Second differences: 8, 14, 20. Third differences: 6, 6, so next is 26, making second difference 26, first difference 71, giving 84+71=155.

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