Introduction to Finding Missing Terms

Hello Year 6! Today, we’re going to learn about finding missing terms in a sequence. A sequence is simply a list of numbers that follow a certain pattern. Sometimes, we may not know one or more numbers in the sequence. Our job is to figure them out!

What is a Sequence?

A sequence can be made by adding, subtracting, multiplying, or dividing numbers. For example, if we start with the number 2 and keep adding 3, our sequence will look like this:

  • 2, 5, 8, 11, …

In this sequence, we can see that we add 3 each time.

Types of Sequences

  1. Additive sequences: Each term is made by adding a number to the previous one.
    • Example: 2, 4, 6, 8,… (Here, we add 2 each time)
  2. Subtractive sequences: Each term is made by subtracting a number from the previous one.
    • Example: 10, 8, 6, 4,… (Here, we subtract 2 each time)
  3. Multiplicative sequences: Each term is made by multiplying the previous term by a number.
    • Example: 3, 6, 12, 24,… (Here, we multiply by 2 each time)
  4. Divisive sequences: Each term is made by dividing the previous term by a number.
    • Example: 64, 32, 16, 8,… (Here, we divide by 2 each time)

Finding the Missing Terms

To find a missing term, you need to identify the pattern in the sequence. Here are the steps to follow:

  1. Look for a pattern: See how the numbers change from one term to the next.
  2. Use the pattern: Apply the same operation to find the missing number.
  3. Check your work: Make sure your answer fits the pattern.

Example 1: Finding a Missing Additive Term

Let’s look at this sequence:

  • 5, ___, 15, 20

To find the missing term, we notice that the sequence increases.

  1. From 15 to 20, we add 5.
  2. So, we must add 5 to the term before 15.
  3. Therefore, 15 – 5 = 10.

So the complete sequence is: 5, 10, 15, 20.

Example 2: Finding a Missing Multiplicative Term

Consider this sequence:

  • 3, 6, ___, 24

Here, we can see:

  1. From 3 to 6, we multiply by 2.
  2. From 6 to the missing term, we will also multiply by 2.
  3. Therefore, 6 × 2 = 12.

The complete sequence is: 3, 6, 12, 24.

Tips and Tricks

  • Write down the differences: If you’re unsure about the pattern, write down how much each term changes.
  • Look for multiplication or division: If the numbers are getting bigger quickly, you might be multiplying. If they’re getting smaller, check for division.
  • Practice, practice, practice: The more you work with sequences, the easier it gets to spot the patterns!

Questions

Easy Level Questions

  1. 2, ___, 6
  2. 10, 20, ___, 40
  3. 5, 10, 15, ___
  4. 1, 2, 3, ___
  5. 7, ___, 9
  6. 4, 8, ___, 16
  7. ___, 3, 4, 5
  8. 12, ___, 18
  9. 0, 1, 2, ___
  10. 14, ___, 18
  11. 3, 6, ___
  12. ___, 9, 12
  13. 8, 6, ___, 0
  14. ___, 2, 4, 6
  15. 1, 3, ___, 7
  16. 5, 5, ___, 5
  17. 2, 4, ___, 8
  18. 10, ___, 30
  19. 6, ___, 12
  20. ___, 1, 2, 3

Medium Level Questions

  1. 5, 10, ___, 20
  2. ___, 15, 18, 21
  3. 3, 9, ___, 81
  4. 25, ___, 15, 10
  5. 2, 5, ___, 11
  6. 100, 90, ___, 70
  7. ___, 12, 14, 16
  8. 4, 8, 16, ___
  9. 6, ___, 24
  10. 5, 15, ___, 45
  11. 7, ___, 21
  12. ___, 30, 20
  13. 10, 20, ___, 40
  14. 3, 6, ___, 12
  15. 1, 4, 9, ___
  16. ___, 50, 75, 100
  17. 6, ___, 18
  18. ___, 4, 8, 12
  19. 100, 80, ___, 40
  20. 2, ___, 8, 10

Hard Level Questions

  1. 2, 4, 8, ___, 32
  2. ___, 64, 32, 16
  3. 10, 20, ___, 40
  4. 50, 45, ___, 35
  5. 3, 6, ___, 24
  6. ___, 8, 16, 32
  7. 15, ___, 45, 60
  8. 1, 2, 4, ___, 16
  9. ___, 12, 18, 24
  10. 27, ___, 9, 3
  11. 8, 16, ___, 64
  12. ___, 25, 20, 15
  13. 1, 3, 7, ___
  14. 5, 10, 20, ___
  15. ___, 11, 13, 15
  16. 12, 24, ___, 48
  17. ___, 1.5, 3, 4.5
  18. 9, 27, ___, 243
  19. 2, 6, ___, 54
  20. ___, 10, 20, 30

Answers and Explanations

Easy Level Answers

  1. 4 (2 + 2 = 4)
  2. 30 (20 + 10 = 30)
  3. 20 (15 + 5 = 20)
  4. 4 (3 + 1 = 4)
  5. 8 (7 + 1 = 8)
  6. 12 (8 + 4 = 12)
  7. 2 (1 + 1 = 2)
  8. 15 (12 + 3 = 15)
  9. 3 (2 + 1 = 3)
  10. 16 (14 + 2 = 16)
  11. 9 (6 + 3 = 9)
  12. 6 (9 – 3 = 6)
  13. 4 (6 – 2 = 4)
  14. 0 (2 – 2 = 0)
  15. 5 (3 + 2 = 5)
  16. 5 (5 + 0 = 5)
  17. 6 (4 + 2 = 6)
  18. 20 (10 + 10 = 20)
  19. 9 (6 + 3 = 9)
  20. 0 (1 – 1 = 0)

Medium Level Answers

  1. 15 (10 + 5 = 15)
  2. 12 (15 – 3 = 12)
  3. 27 (9 × 3 = 27)
  4. 20 (25 – 5 = 20)
  5. 8 (5 + 3 = 8)
  6. 80 (90 – 10 = 80)
  7. 10 (12 – 2 = 10)
  8. 32 (16 × 2 = 32)
  9. 12 (6 × 2 = 12)
  10. 30 (15 × 2 = 30)
  11. 14 (7 × 2 = 14)
  12. 25 (30 – 5 = 25)
  13. 30 (20 + 10 = 30)
  14. 9 (6 + 3 = 9)
  15. 16 (9 + 7 = 16)
  16. 75 (50 + 25 = 75)
  17. 12 (6 × 2 = 12)
  18. 0 (12 – 12 = 0)
  19. 60 (80 – 20 = 60)
  20. 6 (2 + 4 = 6)

Hard Level Answers

  1. 16 (8 × 2 = 16)
  2. 128 (64 × 2 = 128)
  3. 30 (20 + 10 = 30)
  4. 40 (45 – 5 = 40)
  5. 12 (6 × 2 = 12)
  6. 4 (8 ÷ 2 = 4)
  7. 30 (15 × 2 = 30)
  8. 8 (4 × 2 = 8)
  9. 6 (12 – 6 = 6)
  10. 9 (27 ÷ 3 = 9)
  11. 32 (16 × 2 = 32)
  12. 10 (25 – 15 = 10)
  13. 15 (7 + 8 = 15)
  14. 40 (20 × 2 = 40)
  15. 9 (7 + 2 = 9)
  16. 36 (24 + 12 = 36)
  17. 0.75 (1.5 ÷ 2 = 0.75)
  18. 81 (27 × 3 = 81)
  19. 18 (6 × 3 = 18)
  20. 1 (10 ÷ 10 = 1)

I hope you all enjoyed this lesson on finding missing terms! Keep practicing, and you’ll become an expert in no time!