Complete the Sequence: Finding Missing Numbers in 12 __ 10 __ 8 7 6 5 4 3 2 1

Number Sequences with Descending Patterns

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:13 Let's fill in the missing pieces together.
00:16 First, notice the difference between each item. We call this difference, D.
00:28 Now, complete it according to the pattern we discovered.
00:38 Let's continue with the same pattern by adding 1.
00:45 And there you have it! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

2

Step-by-step solution

It is possible to see that there is a difference of one number between each number.

That is, 1 is added to each number and it will be the next number:

1+1=2 1+1=2

2+1=3 2+1=3

3+1=4 3+1=4

Etcetera. Therefore, the next numbers missing in the sequence will be:8+1=9 8+1=9

10+1=11 10+1=11

3

Final Answer

11 , 9

Key Points to Remember

Essential concepts to master this topic
  • Rule: Descending sequences decrease by a constant difference each term
  • Technique: Work backwards: 8+1=9, then 10+1=11 for missing values
  • Check: Verify pattern holds: 12,11,10,9,8,7,6,5,4,3,2,1 decreases by 1 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting to find pattern
    Don't add 1 going from left to right like 12+1=13! This creates an increasing sequence when you need decreasing. Always subtract 1 as you move right: 12-1=11, 11-1=10, 10-1=9.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

How do I know if a sequence is increasing or decreasing?

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Look at the given numbers first! Here we see 12...10...8,7,6,5,4,3,2,1 getting smaller, so it's decreasing. The numbers go down by 1 each time.

What if I can't see the pattern right away?

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Start with the consecutive numbers you can see clearly! From 8,7,6,5,4,3,2,1, the difference is -1. Then work backwards to fill the gaps.

Why can't the missing numbers be 10 and 9?

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That would give us 12,10,10,9,8... which means going from the first 10 to the second 10 has zero difference, breaking the pattern of decreasing by 1.

How do I check if my sequence is correct?

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Count the differences between every consecutive pair: 12-11=1, 11-10=1, 10-9=1, 9-8=1, etc. They should all be the same!

What does 'term-to-term rule' mean?

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It means there's a consistent pattern between each number and the next one. In this case, each term is 1 less than the previous term.

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