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Practice set

Number Sequences • Hard 1 Set

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Answer key & explanations

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NS-013 • Difficulty 1/5

Find the next number: 4, 12, 36, 108, 324, ?

Answer: 972

Rule: The pattern is geometric: multiply by 3 each step.

So the next number is 972.

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NS-008 • Difficulty 2/5

Find the next number: 4, 8, 16, 32, 64, ?

Answer: 128

Rule: The pattern is geometric: multiply by 2 each step.

So the next number is 128.

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NS-015 • Difficulty 2/5

Find the next number: 1, 5, 9, 13, 17, ?

Answer: 21

Rule: The pattern is an arithmetic sequence: add 4 each step.

So the next number is 21.

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NS-010 • Difficulty 4/5

Find the next number: 13, 15, 19, 25, 33, ?

Answer: 43

Rule: The gaps increase by 2 each time: +2, +4, +6, +8, then +10.

So the next number is 43.

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NS-012 • Difficulty 4/5

Find the next number: 1, 8, 9, 17, 26, ?

Answer: 43

Rule: This follows a Fibonacci-like rule: each term is the sum of the previous two.

So the next number is 43.

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NS-005 • Difficulty 5/5

Find the next number: 7, 17, 27, 37, 47, ?

Answer: 57

Rule: The pattern is an arithmetic sequence: add 10 each step.

So the next number is 57.

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NS-006 • Difficulty 5/5

Find the next number: 9, 21, 24, 36, 39, ?

Answer: 51

Rule: The pattern alternates: +12, +3, +12, +3, ... so the next step is +12.

So the next number is 51.

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NS-016 • Difficulty 5/5

Find the next number: 11, 13, 17, 23, 31, ?

Answer: 41

Rule: The gaps increase by 2 each time: +2, +4, +6, +8, then +10.

So the next number is 41.

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NS-018 • Difficulty 5/5

Find the next number: 4, 14, 44, 134, 404, ?

Answer: 1214

Rule: Apply two steps repeatedly: ×3 then +2.

So the next number is 1214.

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NS-021 • Difficulty 5/5

Find the next number: 1, 3, 9, 27, 81, ?

Answer: 243

Rule: The pattern is geometric: multiply by 3 each step.

So the next number is 243.

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