Identify the Next Numbers in the Sequence: 20,155, 20,154, 20,153, ...

Arithmetic Sequences with Decreasing Pattern

Complete the sequence:

20,155, 20,154, 20,153,  20{,}155,\ 20{,}154,\ 20{,}153, \ \ldots

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the sequence:

20,155, 20,154, 20,153,  20{,}155,\ 20{,}154,\ 20{,}153, \ \ldots

2

Step-by-step solution

To complete the sequence 20,155,20,154,20,153, 20{,}155, 20{,}154, 20{,}153, \ldots , follow these steps:

  • Step 1: Identify the sequence pattern.
  • Step 2: Notice that each term decreases by 1 from the previous term.
  • Step 3: Continue the pattern by subtracting 1 from the last known term.

Let's work through the steps:

Step 1:
The sequence given is: 20,155,20,154,20,153, 20{,}155, 20{,}154, 20{,}153, \ldots .
Step 2:
Observe that the first term 20,155 20{,}155 is reduced to 20,154 20{,}154 , then to 20,153 20{,}153 , establishing a pattern of subtracting 1.
Step 3:
Using this pattern, find the next terms:
From 20,153 20{,}153 , subtract 1 to get 20,152 20{,}152 .
From 20,152 20{,}152 , subtract 1 to get 20,151 20{,}151 .
From 20,151 20{,}151 , subtract 1 to get 20,150 20{,}150 .

Therefore, the sequence continues as follows: 20,152,20,151,20,150 20{,}152, 20{,}151, 20{,}150 .

3

Final Answer

20,152, 20,151, 20,150 20{,}152,\ 20{,}151,\ 20{,}150

Key Points to Remember

Essential concepts to master this topic
  • Pattern: Identify the common difference between consecutive terms
  • Technique: 20,155 - 20,154 = -1, so subtract 1 each time
  • Check: Verify pattern holds: 20,153 - 1 = 20,152 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of continuing the decreasing pattern
    Don't add 1 to get 20,154, 20,155, 20,156 = wrong direction! This ignores the established decreasing pattern. Always identify whether the sequence increases or decreases before continuing.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

\( 20{,}000,\ 20{,}001,\ 20{,}002, \ \ldots \)

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 first few terms! If each number gets smaller (like 20,155 → 20,154 → 20,153), it's decreasing. If each gets larger, it's increasing.

What if the pattern isn't adding or subtracting 1?

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Find the common difference by subtracting any term from the next one. It could be +2, -3, +5, etc. The key is that this difference stays the same throughout the sequence.

How many terms should I find to complete the sequence?

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Usually 3 terms unless the problem specifies more. This shows you understand the pattern and can apply it multiple times correctly.

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

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Write out the differences between consecutive terms: 20,15420,155=1 20,154 - 20,155 = -1 and 20,15320,154=1 20,153 - 20,154 = -1 . When differences are equal, you've found your pattern!

Can arithmetic sequences have negative numbers?

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Absolutely! If you keep subtracting from positive numbers, you'll eventually reach zero and then negative numbers. The pattern still works the same way.

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