Pattern Rules From Sequences

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SSAT Middle Level: Quantitative › Pattern Rules From Sequences

Questions 1 - 10
1

What is the rule for $8, 12, 18, 27, 40, 60$?

Add 4 each time

Multiply by 2 each time

Add 4, 6, 9, 13, 20

Subtract 4 each time

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, the differences are 4, 6, 9, 13, 20, which may follow an approximate multiplication by 1.5 with adjustments. Choice A is correct because it accurately lists the additions that generate the sequence, showing understanding of variable differences. Choice B is incorrect because it suggests multiplying by 2 each time, reflecting a common misconception of assuming a geometric progression. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

2

Explain how the sequence is formed: $20, 18, 21, 19, 22, 20$.

Multiply by 2 each time

Subtract 2, then add 3

Add 1 each time

Add 2, then subtract 3

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, the pattern alternates between subtracting 2 and adding 3. Choice A is correct because it accurately describes the sequence's rule, showing understanding of alternating operations. Choice B is incorrect because it reverses the operations, reflecting a common misconception of misordering the pattern. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

3

Predict the next number: $11, 14, 12, 15, 13, 16, ;?$

10

14

15

17

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, the pattern alternates between adding 3 and subtracting 2. Choice A is correct because it accurately predicts the next number as 14, showing understanding of the alternating pattern. Choice B is incorrect because it suggests 15, reflecting a common misconception of continuing addition without the subtraction. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

4

What is the rule for $100, 90, 80, 70, 60$?

Subtract 10 each time

Subtract 5 each time

Divide by 10 each time

Add 10 each time

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is decreased by 10 to produce the next. Choice B is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a common difference of -10. Choice A is incorrect because it suggests subtracting 5, reflecting a common misconception of halving the actual difference. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

5

Explain how the sequence is formed: $30, 27, 24, 21, 18$.

Subtract 6 each time

Multiply by 3 each time

Add 3 each time

Subtract 3 each time

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is decreased by 3 to produce the next. Choice A is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a negative common difference. Choice B is incorrect because it suggests adding 3, reflecting a common misconception of reversing the direction of change. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

6

What operation is used to generate $3, 6, 12, 24, 48$?

Add 3 each time

Multiply by 3 each time

Multiply by 2 each time

Subtract 3 each time

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is multiplied by 2 to produce the next. Choice B is correct because it accurately describes the sequence's rule, showing understanding of geometric progression with a common ratio of 2. Choice A is incorrect because it suggests adding 3 each time, reflecting a common misconception of confusing multiplication with addition. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

7

What is the rule for $6, 11, 16, 21, 26$?

Add 5 each time

Subtract 5 each time

Add 4 each time

Multiply by 5 each time

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is increased by 5 to produce the next. Choice B is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a common difference of 5. Choice A is incorrect because it suggests adding 4, reflecting a common misconception of undercalculating the difference. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

8

Identify the pattern rule for $4, 9, 14, 19, 24, 29$.

Add 5 each time

Add 4 each time

Multiply by 2 each time

Add 5, then add 4

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is increased by 5 to produce the next. Choice C is correct because it accurately describes the sequence's rule, showing understanding of arithmetic progression with a common difference of 5. Choice A is incorrect because it suggests adding 4 each time, reflecting a common misconception of miscalculating the constant difference. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

9

Predict the next number: $9, 18, 36, 72, ;?$

81

90

108

144

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, each number is multiplied by 2 to produce the next. Choice C is correct because it accurately predicts the next number as 144, showing understanding of geometric progression with a common ratio of 2. Choice A is incorrect because it suggests 81, reflecting a common misconception of switching to a different ratio like 9 times something. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

10

Identify the pattern in $5, 8, 6, 9, 7, 10$.

Add 3 each time

Add 1 each time

Add 3, then subtract 2

Subtract 3, then add 2

Explanation

This question tests SSAT Middle Level skills: identifying pattern rules from sequences. Patterns and sequences involve recognizing regular structures in numbers or shapes, often expressed as arithmetic or geometric progressions. In this sequence, the pattern alternates between adding 3 and subtracting 2. Choice B is correct because it accurately describes the sequence's rule, showing understanding of alternating operations in a pattern. Choice D is incorrect because it suggests adding 1 each time, reflecting a common misconception of averaging the net change. To help students: Encourage them to identify what changes between elements—look for operations or transformations. Practice with mixed sequences to see different types of patterns. Watch for: over-simplifying complex patterns or confusing similar operations.

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