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ISEE Lower Level Mathematics Achievement Quiz

ISEE Lower Level Mathematics Achievement Quiz: Missing Number In Sequences

Practice Missing Number In Sequences in ISEE Lower Level Mathematics Achievement with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

Question 1 / 18

0 of 18 answered

What number completes the sequence: 30, 25, ‾\underline{\hspace{2em}}​, 15, 10?

Select an answer to continue

What this quiz covers

This quiz focuses on Missing Number In Sequences, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

What number completes the sequence: 30, 25, ‾\underline{\hspace{2em}}​, 15, 10?

  1. 18
  2. 20 (correct answer)
  3. 22
  4. 24

Explanation: This question tests ISEE Lower Level Mathematics: finding the missing number in an arithmetic sequence. An arithmetic sequence is a list of numbers with a constant difference between consecutive numbers, and understanding this requires identifying the pattern and applying it to find missing terms. In this specific sequence, [30, 25, _, 15, 10], the difference is -5, meaning each number decreases by 5. The correct answer, 20, fits the pattern because 25 - 5 = 20, and 20 - 5 = 15, continuing the descending sequence correctly. A common distractor, such as 22, might seem correct if students miscalculate the difference or don't maintain consistency. To teach this skill, practice skip counting backwards by 5s, use visual aids like number lines to show the regular intervals, and remind students to verify their pattern works for all consecutive pairs in the sequence.

Question 2

Maya is saving money. She puts 15.50inherpiggybankinthefirstweek.Eachweekafterthat,shesaves15.50 in her piggy bank in the first week. Each week after that, she saves 15.50inherpiggybankinthefirstweek.Eachweekafterthat,shesaves3.50 more than the week before. How much money will she save in the fourth week alone?

  1. $22.50
  2. $26.00 (correct answer)
  3. $29.50
  4. $83.00

Explanation: The correct answer is 26.00.Thequestionasksfortheamountsavedinthefourthweek,notthetotalsaved.Thesequencerepresentstheamountsavedeachweek.Week1:26.00. The question asks for the amount saved in the fourth week, not the total saved. The sequence represents the amount saved each week. Week 1: 26.00.Thequestionasksfortheamountsavedinthefourthweek,notthetotalsaved.Thesequencerepresentstheamountsavedeachweek.Week1:15.50. Week 2: 15.50+15.50 + 15.50+3.50 = 19.00.Week3:19.00. Week 3: 19.00.Week3:19.00 + 3.50=3.50 = 3.50=22.50. Week 4: 22.50+22.50 + 22.50+3.50 = $26.00.

Question 3

The numbers in a sequence are 105, 98, 91, 84, ... If the pattern of subtracting the same number continues, what will be the 7th number in the sequence?

  1. 70
  2. 63 (correct answer)
  3. 56
  4. 49

Explanation: The correct answer is 63. The rule for the sequence is to subtract 7 each time (105 - 7 = 98). The terms are: 1st=105, 2nd=98, 3rd=91, 4th=84, 5th=77, 6th=70, 7th=63.

Question 4

Ken practices piano for 20 minutes on Monday, 26 minutes on Tuesday, and 32 minutes on Wednesday. If he continues to increase his practice time by the same number of minutes each day, how many minutes will he practice on Sunday of that same week?

  1. 44
  2. 50
  3. 56 (correct answer)
  4. 62

Explanation: The correct answer is 56. The pattern is an arithmetic sequence. The common difference is 26 - 20 = 6 minutes. The sequence of practice times is: Mon=20, Tue=26, Wed=32, Thu=38, Fri=44, Sat=50, Sun=56.

Question 5

In an arithmetic sequence, the first term is 14 and the fourth term is 44. What is the second term?

  1. 20
  2. 24 (correct answer)
  3. 29
  4. 34

Explanation: The correct answer is 24. The difference between the fourth term (44) and the first term (14) is 30. This difference occurs over 3 steps (from term 1 to term 4). The common difference is 30 ÷ 3 = 10. The second term is the first term plus the common difference: 14 + 10 = 24.

Question 6

A crystal is growing in a science experiment. On Day 2, its mass is 18 grams. On Day 6, its mass is 42 grams. If it grows by the same amount each day, what was its mass on Day 4?

  1. 24 grams
  2. 25 grams
  3. 30 grams (correct answer)
  4. 36 grams

Explanation: The correct answer is 30 grams. The crystal's mass increased by 42 - 18 = 24 grams over 4 days (from Day 2 to Day 6). The daily growth is 24 grams ÷ 4 days = 6 grams per day. The mass on Day 3 would be 18 + 6 = 24 grams. The mass on Day 4 would be 24 + 6 = 30 grams.

Question 7

A swimming pool is being drained. At 1:00 PM, it has 5,000 gallons of water. At 3:00 PM, it has 4,200 gallons. If the water drains at a constant rate, how many gallons were in the pool at 2:00 PM?

  1. 4,800
  2. 4,600 (correct answer)
  3. 4,500
  4. 4,400

Explanation: The correct answer is 4,600. In the 2 hours between 1:00 PM and 3:00 PM, the amount of water decreased by 5,000 - 4,200 = 800 gallons. Since the rate is constant, the pool drains 800 ÷ 2 = 400 gallons each hour. At 2:00 PM, one hour after 1:00 PM, the amount of water would be 5,000 - 400 = 4,600 gallons.

Question 8

The third term of an arithmetic sequence is 25 and the fifth term is 43. What is the first term?

  1. 7 (correct answer)
  2. 9
  3. 16
  4. 34

Explanation: The correct answer is 7. The difference between the fifth term (43) and the third term (25) is 18. This occurs over 2 steps, so the common difference is 18 ÷ 2 = 9. To find the first term, we work backward from the third term. The third term is 25. The second term is 25 - 9 = 16. The first term is 16 - 9 = 7.

Question 9

A baker starts the day with 120 cookies. He sells a fixed number of cookies every hour. After 3 hours, he has 84 cookies left. If this pattern continues, how many cookies will he have left after 5 hours?

  1. 48
  2. 36
  3. 72
  4. 60 (correct answer)

Explanation: When you encounter a problem about constant rates of change over time, you're working with linear patterns. The key is to find the rate first, then extend the pattern. Let's find how many cookies the baker sells per hour. He started with 120 cookies and had 84 left after 3 hours, so he sold 120−84=36120 - 84 = 36120−84=36 cookies in 3 hours. This means he sells 36÷3=1236 ÷ 3 = 1236÷3=12 cookies per hour. Now we can find how many cookies he'll have after 5 hours. In 5 hours, he'll sell 12×5=6012 × 5 = 6012×5=60 cookies total. Starting with 120 cookies, he'll have 120−60=60120 - 60 = 60120−60=60 cookies remaining. Looking at the wrong answers: Choice A (48) represents what you'd get if you incorrectly assumed he sells 36 cookies every 3-hour period, so after 6 hours he'd have 48 left—but the question asks about 5 hours. Choice B (36) is the total number of cookies sold in the first 3 hours, not what's remaining after 5 hours. Choice C (72) is what he'd have left after just 4 hours (120 - 48 = 72), showing a calculation that stopped one hour short. For rate problems like this, always identify the unit rate first (cookies per hour), then multiply by the total time period. Double-check by working backwards: if he has 60 cookies left after selling 12 per hour for 5 hours, he must have started with 60 + 60 = 120 cookies, which matches the given information.

Question 10

At a school fundraiser, the first prize is 250.Thesecondprizeis250. The second prize is 250.Thesecondprizeis225. The third prize is $200. If this pattern continues for all the prizes, what is the value of the eighth prize?

  1. $100
  2. $75 (correct answer)
  3. $50
  4. $25

Explanation: The correct answer is 75.Thesequenceofprizemoneydecreasesbyaconstantamount.Thecommondifferenceis75. The sequence of prize money decreases by a constant amount. The common difference is 75.Thesequenceofprizemoneydecreasesbyaconstantamount.Thecommondifferenceis225 - 250=−250 = -250=−25. The rule is to subtract 25foreachsubsequentprize.Theprizesare:1st=25 for each subsequent prize. The prizes are: 1st=25foreachsubsequentprize.Theprizesare:1st=250, 2nd=225,3rd=225, 3rd=225,3rd=200, 4th=175,5th=175, 5th=175,5th=150, 6th=125,7th=125, 7th=125,7th=100, 8th=$75.

Question 11

The second, third, and fourth terms of an arithmetic sequence are 4.5, 6, and 7.5. What is the first term?

  1. 1.5
  2. 3 (correct answer)
  3. 3.5
  4. 9

Explanation: The correct answer is 3. First, find the common difference by subtracting consecutive terms: 6 - 4.5 = 1.5. To find the first term, subtract the common difference from the second term: 4.5 - 1.5 = 3.

Question 12

A library fine for an overdue book is 0.35forthefirstday.Eachadditionaldayaddsaconstantamounttothetotalfine.Ifthefineforabook3daysoverdueis0.35 for the first day. Each additional day adds a constant amount to the total fine. If the fine for a book 3 days overdue is 0.35forthefirstday.Eachadditionaldayaddsaconstantamounttothetotalfine.Ifthefineforabook3daysoverdueis0.85, what is the fine for a book 6 days overdue?

  1. $1.10
  2. $1.35
  3. $1.60 (correct answer)
  4. $1.70

Explanation: The correct answer is 1.60.Thefineforday1is1.60. The fine for day 1 is 1.60.Thefineforday1is0.35 and for day 3 is 0.85.Theincreaseover2daysis0.85. The increase over 2 days is 0.85.Theincreaseover2daysis0.85 - 0.35=0.35 = 0.35=0.50. So, the constant amount added each day is 0.50÷2=0.50 ÷ 2 = 0.50÷2=0.25. The fines are: Day 1=0.35,Day2=0.35, Day 2=0.35,Day2=0.60, Day 3=0.85,Day4=0.85, Day 4=0.85,Day4=1.10, Day 5=1.35,Day6=1.35, Day 6=1.35,Day6=1.60.

Question 13

Find the missing term: 4, 9, ‾\underline{\hspace{2em}}​, 19, 24.

  1. 12
  2. 15
  3. 13
  4. 14 (correct answer)

Explanation: This question tests ISEE Lower Level Mathematics: finding the missing number in an arithmetic sequence. An arithmetic sequence is a list of numbers with a constant difference between consecutive numbers, and understanding this requires identifying the pattern and applying it to find missing terms. In this specific sequence, [4, 9, _, 19, 24], the difference is 5, meaning each number increases by 5. The correct answer, 14, fits the pattern because 9 + 5 = 14, and 14 + 5 = 19, maintaining the consistent increase throughout. A common distractor, such as 15, might seem correct if students look at the middle position without calculating the actual pattern. To teach this skill, have students find differences between all given consecutive pairs first, practice adding 5 mentally, and always double-check by ensuring the pattern works both forward and backward from the missing number.

Question 14

A pattern is made of tiles. The sequence of the number of tiles in the first six designs is 5, 9, 13, ‾\underline{\hspace{2em}}​, 21, 25. What is the number of tiles in the missing design?

  1. 15
  2. 17 (correct answer)
  3. 18
  4. 19

Explanation: The correct answer is 17. By observing the given numbers, we can find the pattern. The difference between 9 and 5 is 4. The difference between 13 and 9 is 4. The difference between 25 and 21 is 4. The rule is to add 4 to the previous term. The missing number is 13 + 4 = 17. To check, 17 + 4 = 21.

Question 15

A five-term arithmetic sequence is 28, 37, 46, ‾\underline{\hspace{2em}}​, 64. What is the missing number?

  1. 54
  2. 55 (correct answer)
  3. 56
  4. 57

Explanation: The correct answer is 55. To find the rule of the sequence, subtract any term from the one that follows it. For example, 37 - 28 = 9. The rule is to add 9. The missing number is the fourth term, which is 46 + 9 = 55. To check, add 9 to 55: 55 + 9 = 64, which is the fifth term.

Question 16

The numbers 18, ‾\underline{\hspace{2em}}​, ‾\underline{\hspace{2em}}​, 54 are part of an arithmetic sequence with two missing terms. What is the first missing number?

  1. 27
  2. 30 (correct answer)
  3. 36
  4. 42

Explanation: The correct answer is 30. The sequence has four terms. The difference between the fourth term (54) and the first term (18) is 36. This difference is spread over 3 steps. The common difference is 36 ÷ 3 = 12. The first missing number (the second term) is 18 + 12 = 30. The sequence is 18, 30, 42, 54.

Question 17

What number completes the sequence: 20, 16, ‾\underline{\hspace{2em}}​, 8, 4?

  1. 14
  2. 10
  3. 12 (correct answer)
  4. 6

Explanation: This question tests ISEE Lower Level Mathematics: finding the missing number in an arithmetic sequence. An arithmetic sequence is a list of numbers with a constant difference between consecutive numbers, and understanding this requires identifying the pattern and applying it to find missing terms. In this specific sequence, [20, 16, _, 8, 4], the difference is -4, meaning each number decreases by 4. The correct answer, 12, fits the pattern because 16 - 4 = 12, and 12 - 4 = 8, maintaining the consistent decrease. A common distractor, such as 14, might seem correct if students mistakenly calculate the difference as -2 or make an arithmetic error. To teach this skill, help students recognize that sequences can decrease as well as increase, practice finding differences in descending sequences, and emphasize the importance of checking that the pattern works for all given terms in the sequence.

Question 18

The numbers 112, 99, ‾\underline{\hspace{2em}}​, 73, 60 form an arithmetic sequence. What is the missing number?

  1. 82
  2. 85
  3. 86 (correct answer)
  4. 87

Explanation: The correct answer is 86. To find the rule, subtract a term from the one before it. 112 - 99 = 13. Or, 73 - 60 = 13. The rule is to subtract 13. The missing number is the third term. To find it, subtract 13 from the second term: 99 - 13 = 86. To check, subtract 13 from the result: 86 - 13 = 73.