Find the next term: 13, 17, 23, 31, 41, ___
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The successive increases are 4, 6, 8, and 10.
The next increase is 12, so 41 + 12 = 53.
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The successive increases are 4, 6, 8, and 10.
The next increase is 12, so 41 + 12 = 53.
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Each term is multiplied by 2.
Therefore, 96 × 2 = 192.
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These are descending squares: 12², 11², 10², and 9².
The next term is 8² = 64.
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The terms are cubes of consecutive integers: 1³, 2³, 3³, and 4³.
The next term is 5³ = 125.
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The operations alternate between adding 2 and multiplying by 2.
After 30, the next operation is ×2, giving 60.
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The differences are 1, 2, 3, and 4.
The next difference is 5, producing 17.
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The subtractions are 2, 3, 4, and 5.
Subtracting 6 from 6 gives 0.
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Each term is twice the previous term plus 1.
So 31 × 2 + 1 = 63.
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The sequence doubles at each step.
Thus, 88 × 2 = 176.
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Each term is half of the preceding term.
Therefore, 8 ÷ 2 = 4.
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Each term is doubled and increased by 1.
So 31 × 2 + 1 = 63.
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The terms are factorials: 1!, 2!, 3!, and 4!.
The next term is 5! = 120.