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

Look at the following set of numbers and determine if there is any property, if so, what is it?

\( 94,96,98,100,102,104 \)

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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