Complete the Decreasing Sequence: 900, 800, and Beyond

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

Compare the first two given terms. If the second number is smaller than the first (like 900,800 decreasing. If it's larger, the sequence is increasing.

Q: What if the difference isn't obvious?

Always calculate: second term - first term. In our example: $ 900,800 - 900,900 = -100 $. The negative sign tells you it's decreasing by 100.

Q: Can the pattern change in the middle of a sequence?

In arithmetic sequences, the pattern stays the same throughout. If you're told it's a sequence, the difference between any two consecutive terms should be constant.

Q: How many terms should I find?

Look at the answer choices! They usually show 3 terms to continue the pattern, so find the next 3 terms using your common difference.

Q: What if I get confused with the commas in large numbers?

Treat $ 900,900 $ as nine hundred thousand, nine hundred. Focus on the numerical difference, not the comma placement when doing calculations.

Arithmetic Sequences with Constant Differences

Complete the sequence:

$900{,}900,\ 900{,}800, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$900{,}900,\ 900{,}800, \ \ldots$

Step-by-step solution

To find the pattern in the sequence $900,900, 900,800, \ldots$ , we need to determine the difference between successive terms.

Step 1: Calculate the difference between the first two terms:

$900,800 - 900,900 = -100$

Step 2: The sequence decreases by 100. Using this consistent decrease, we can determine the next terms:

From $900,800$ , subtract 100: $900,800 - 100 = 900,700$
From $900,700$ , subtract 100: $900,700 - 100 = 900,600$
From $900,600$ , subtract 100: $900,600 - 100 = 900,500$

Therefore, the completed sequence is $900,700, 900,600, 900,500$ .

Final Answer

$900{,}700,\ 900{,}600, \ 900{,}500$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Subtract first term from second: $900,800 - 900,900 = -100$
Check: Verify each step decreases by same amount: 900,700, 900,600, 900,500 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the pattern
Don't add 100 to continue the sequence when it's decreasing = wrong direction! This happens when students see large numbers and assume growth. Always check if the sequence increases or decreases first, then apply the pattern consistently.

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?

Compare the first two given terms. If the second number is smaller than the first (like 900,800 < 900,900), the sequence is decreasing. If it's larger, the sequence is increasing.

What if the difference isn't obvious?

Always calculate: second term - first term. In our example: $900,800 - 900,900 = -100$ . The negative sign tells you it's decreasing by 100.

Can the pattern change in the middle of a sequence?

In arithmetic sequences, the pattern stays the same throughout. If you're told it's a sequence, the difference between any two consecutive terms should be constant.

How many terms should I find?

Look at the answer choices! They usually show 3 terms to continue the pattern, so find the next 3 terms using your common difference.

What if I get confused with the commas in large numbers?

Treat $900,900$ as nine hundred thousand, nine hundred. Focus on the numerical difference, not the comma placement when doing calculations.

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