Multiple choice

What will be the next term in the series? 0, 10, 6, 68, 20, ?

  1. 217

  2. 222

  3. 42

  4. 36

  5. 225
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B Correct answer
Explanation

The series is 0, 10, 6, 68, 20, ?. The pattern is alternating: 0, 6, 20 (n^3 - n) for n=1, 2, 3 (1-1=0, 8-2=6, 27-3=24? No). Let's look at the other terms: 10, 68, ?. 10 = 2^3 + 2, 68 = 4^3 + 4. The next term should be 6^3 + 6 = 216 + 6 = 222.

AI explanation

The series alternates between the cubes of numbers and the squares of numbers, with alternating signs. The terms are 1 cubed minus 1 (0), 3 squared plus 1 (10), 2 cubed minus 2 (6), 4 cubed plus 4 (68), and 5 squared minus 5 (20). Following this pattern, the next term is 6 cubed plus 6, which equals 216 + 6 = 222.

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