Missing Sequence Terms - ISEE Lower Level Quantitative Reasoning

1. Fill in the blank to continue the sequence: 3 8 13 18 __.
   Answer: 23 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 5 to each term. The correct answer is 23 because it continues the pattern of adding 5: 18 + 5 = 23. Choice 22 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding 4 instead of 5. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
2. Identify the missing term in the series: 4 12 36 __.
   Answer: 108 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of multiplying by 3 each time. The correct answer is 108 because it continues the pattern of multiplying by 3: 36 × 3 = 108. Choice 72 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of multiplying by 2 instead of 3. To help students: Practice recognizing arithmetic and geometric patterns. Encourage breaking down sequences into smaller, manageable parts.
3. Identify the missing term in the series: 3 6 12 __.
   Answer: 24 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of multiplying by 2 each time. The correct answer is 24 because it continues the pattern of multiplying by 2: 12 × 2 = 24. Choice 18 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding instead of multiplying. To help students: Practice recognizing arithmetic and geometric patterns. Encourage breaking down sequences into smaller, manageable parts.
4. A sequence of numbers is formed using the rule 'multiply the position number by 4, then subtract 1.' The first number is in position 1, the second is in position 2, and so on. What is the fifth number in this sequence?
   Answer: 19 To find the fifth number, use 5 as the position number in the rule. First, multiply the position number by 4: $5 \times 4 = 20$. Then, subtract 1: $20 - 1 = 19$. The fifth number in the sequence is 19.
5. A growing pattern of numbers is shown: 3, 4, 6, 9, 13, ... If the pattern continues in the same way, what will be the next number?
   Answer: 18 The pattern is to add a number that increases by one each time. To get from 3 to 4, you add 1. To get from 4 to 6, you add 2. From 6 to 9, you add 3. From 9 to 13, you add 4. The next step is to add 5. So, $13 + 5 = 18$.
6. In a number sequence, each number is 6 more than the number before it. If the second number in the sequence is 15, what is the first number?
   Answer: 9 The rule is 'add 6'. To find the number before 15, you must do the opposite operation, which is to subtract 6. The first number is $15 - 6 = 9$. The sequence would start 9, 15, 21, ...
7. What number completes the sequence: 8 13 18 23 __?
   Answer: 28 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 5 to each term. The correct answer is 28 because it continues the pattern of adding 5: 23 + 5 = 28. Choice 27 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding 4 instead of 5. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
8. David created a number pattern that starts with 1. His pattern is 1, 3, 7, 13, 21, ... What is the next number in David's pattern?
   Answer: 31 The pattern is to add an increasing even number each time. From 1 to 3, add 2. From 3 to 7, add 4. From 7 to 13, add 6. From 13 to 21, add 8. The next step is to add the next even number, which is 10. So, $21 + 10 = 31$.
9. The following sequence multiplies by the same whole number to get from one term to the next: 4, 8, ___, 32, 64, ___. What is the sum of the two missing numbers in the sequence?
   Answer: 144 First, find the rule. To get from 4 to 8, you multiply by 2. Let's check: $8 \times 2 = 16$ and $16 \times 2 = 32$. The rule is 'multiply by 2'. The first missing number is 16. The second missing number comes after 64: $64 \times 2 = 128$. The sum of the two missing numbers is $16 + 128 = 144$.
10. A sequence of numbers is created so that each number is the sum of the two numbers before it. The sequence starts with 1, 4, 5, 9, 14, ... What is the next number in this sequence?
    Answer: 23 The rule is to add the two previous numbers to get the next one. The last two numbers given are 9 and 14. To find the next number, add them together: $9 + 14 = 23$.
11. What number completes the sequence: 1 4 7 10 __?
    Answer: 13 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 3 to each term. The correct answer is 13 because it continues the pattern of adding 3: 10 + 3 = 13. Choice 12 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding 2 instead of 3. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
12. Fill in the blank to continue the sequence: 25 20 25 20 __.
    Answer: 25 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of alternating between 25 and 20. The correct answer is 25 because it continues the pattern of alternating: after 20 comes 25. Choice 15 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of subtracting further. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
13. A sequence of numbers follows a special rule related to its order. The sequence is 1, 4, 9, 16, 25, ... What is the next number if the pattern continues?
    Answer: 36 The numbers in the sequence are perfect squares. The first number is $1 \times 1 = 1$. The second is $2 \times 2 = 4$. The third is $3 \times 3 = 9$. The fourth is $4 \times 4 = 16$. The fifth is $5 \times 5 = 25$. The next number will be the sixth in the sequence, which is $6 \times 6 = 36$.
14. Fill in the blank to continue the sequence: 9 14 19 24 __.
    Answer: 29 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 5 to each term. The correct answer is 29 because it continues the pattern of adding 5: 24 + 5 = 29. Choice 28 is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding 4 instead of 5. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
15. A number sequence starts with 7. The third term is 21 and the fourth term is 28. If the sequence follows the same pattern of adding a number each time, what is the second term?
    Answer: 14 The pattern involves adding the same number to get each term. From the third term (21) to the fourth term (28), the number added is $28 - 21 = 7$. To find the second term, subtract 7 from the third term: $21 - 7 = 14$. To check, the sequence would be 7, 14, 21, 28, which follows the pattern of adding 7 each time.
16. What number completes the sequence: 9 13 17 21 __?
    Answer: 25 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 4 to each term (9+4=13, 13+4=17, 17+4=21). The correct answer is 25 because it continues the pattern of adding 4 to the previous term (21+4=25). Choice A (24) is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding only 3 instead of 4. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
17. What number completes the sequence: 8 12 16 20 __?
    Answer: 24 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 4 to each term (8+4=12, 12+4=16, 16+4=20). The correct answer is 24 because it continues the pattern of adding 4 to the previous term (20+4=24). Choice A (21) is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding only 1 instead of 4. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.
18. A sequence of numbers is created by taking half of the previous number. The sequence begins: 80, 40, 20, 10, ... What is the next number in this sequence?
    Answer: 5 The rule is to divide by 2 (or take half) to find the next term. Half of 80 is 40. Half of 40 is 20. Half of 20 is 10. The next number is half of 10, which is $10 \div 2 = 5$.
19. A pattern of numbers is shown: 5, 8, 12, 17, ... If the pattern continues by adding a greater whole number each time, what is the next number?
    Answer: 23 The pattern is to add a number that increases by 1 each time. From 5 to 8, you add 3. From 8 to 12, you add 4. From 12 to 17, you add 5. The next step is to add 6. So, $17 + 6 = 23$.
20. What comes next in the pattern: 5 9 13 17 __?
    Answer: 21 This question tests ISEE Lower Level quantitative reasoning skills: finding a missing term in a sequence. Understanding sequences involves identifying the pattern that determines each term. In this question, the sequence follows a pattern of adding 4 to each term (5+4=9, 9+4=13, 13+4=17). The correct answer is 21 because it continues the pattern of adding 4 to the previous term (17+4=21). Choice A (20) is incorrect because it fails to apply the pattern consistently and demonstrates a common error of adding only 3 instead of 4. To help students: Practice recognizing arithmetic and geometric patterns. Use number lines to visualize basic sequences.

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