Predicting Sequence Terms
Help Questions
ISEE Upper Level: Mathematics Achievement › Predicting Sequence Terms
An arithmetic sequence increases by 9 each term: $3, 12, 21, 30, 39, \dots$; what is next?
45
46
47
48
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 3, 12, 21, 30, 39, ..., the pattern is an arithmetic sequence with a common difference of 9. Choice D is correct because it accurately applies the arithmetic formula to predict the next term, 39 + 9 = 48, reflecting understanding of sequence growth. Choice A is incorrect because it assumes a smaller difference, which often happens when students average incorrectly. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
An arithmetic sequence has common difference 8: $12, 20, 28, 36, 44, \dots$; what is next?
50
51
52
54
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 12, 20, 28, 36, 44, ..., the pattern is an arithmetic sequence with a common difference of 8. Choice C is correct because it accurately applies the arithmetic formula to predict the next term, 44 + 8 = 52, reflecting understanding of sequence growth. Choice D is incorrect because it assumes a difference of 10, which often happens when students round the difference incorrectly. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
In a geometric sequence, each term is multiplied by 3: $2, 6, 18, 54, 162, \dots$; what is next?
324
486
540
648
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 2, 6, 18, 54, 162, ..., the pattern is a geometric sequence with a common ratio of 3. Choice B is correct because it accurately applies the geometric formula to predict the next term, 162 × 3 = 486, reflecting understanding of sequence growth. Choice A is incorrect because it assumes a ratio of 2, which often happens when students confuse multiplication with addition. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
In an arithmetic sequence, each term increases by 6: $5, 11, 17, 23, 29, \dots$; what is next?
34
35
36
41
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 5, 11, 17, 23, 29, ..., the pattern is an arithmetic sequence with a common difference of 6. Choice B is correct because it accurately applies the arithmetic formula to predict the next term, 29 + 6 = 35, reflecting understanding of sequence growth. Choice A is incorrect because it assumes a difference of 5 instead of 6, which often happens when students miscalculate the common difference. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
A geometric sequence has ratio 5: $3, 15, 75, 375, 1,875, \dots$; what is next?
7,500
10,000
9,375
9,000
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 3, 15, 75, 375, 1,875, ..., the pattern is a geometric sequence with a common ratio of 5. Choice C is correct because it accurately applies the geometric formula to predict the next term, 1,875 × 5 = 9,375, reflecting understanding of sequence growth. Choice D is incorrect because it assumes a ratio of 5.33, which often happens when students divide incorrectly. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
A geometric sequence multiplies by 8: $1, 8, 64, 512, 4,096, \dots$; what is next?
36,864
24,576
32,768
28,672
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 1, 8, 64, 512, 4,096, ..., the pattern is a geometric sequence with a common ratio of 8. Choice C is correct because it accurately applies the geometric formula to predict the next term, 4,096 × 8 = 32,768, reflecting understanding of sequence growth. Choice A is incorrect because it assumes a ratio of 6, which often happens when students underestimate the multiplier. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
In an arithmetic sequence, each term increases by 11: $9, 20, 31, 42, 53, \dots$; what is next?
62
64
66
68
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 9, 20, 31, 42, 53, ..., the pattern is an arithmetic sequence with a common difference of 11. Choice B is correct because it accurately applies the arithmetic formula to predict the next term, 53 + 11 = 64, reflecting understanding of sequence growth. Choice A is incorrect because it assumes a difference of 9, which often happens when students misadd. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
In an arithmetic sequence, each term decreases by 5: $40, 35, 30, 25, 20, \dots$; what is next?
10
12
15
16
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 40, 35, 30, 25, 20, ..., the pattern is an arithmetic sequence with a common difference of -5. Choice C is correct because it accurately applies the arithmetic formula to predict the next term, 20 - 5 = 15, reflecting understanding of sequence growth. Choice D is incorrect because it assumes a difference of -4, which often happens when students miscount the differences. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
A geometric sequence has common ratio 10: $1, 10, 100, 1,000, 10,000, \dots$; what is next?
50,000
110,000
100,000
20,000
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 1, 10, 100, 1,000, 10,000, ..., the pattern is a geometric sequence with a common ratio of 10. Choice C is correct because it accurately applies the geometric formula to predict the next term, 10,000 × 10 = 100,000, reflecting understanding of sequence growth. Choice D is incorrect because it adds instead of multiplying, which often happens when students confuse sequence types. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.
In a geometric sequence, each term is multiplied by 4: $1, 4, 16, 64, 256, \dots$; what is next?
768
1,024
512
1,280
Explanation
This question tests ISEE Upper Level Mathematics Achievement: Predicting future terms in a sequence. Predicting sequence terms involves identifying patterns and applying appropriate formulas. Arithmetic sequences increase by a constant difference, while geometric sequences grow by a constant ratio. In this specific sequence, 1, 4, 16, 64, 256, ..., the pattern is a geometric sequence with a common ratio of 4. Choice C is correct because it accurately applies the geometric formula to predict the next term, 256 × 4 = 1,024, reflecting understanding of sequence growth. Choice A is incorrect because it assumes a ratio of 2, which often happens when students halve the actual ratio. To help students: Practice identifying sequence types and applying corresponding formulas. Encourage checking calculations and understanding the pattern contextually. Use real-world examples to reinforce concepts.