Number Pattern Challenge: Continue the Sequence from 850,000, 750,000

Q: How do I find the pattern when only two terms are given?

Subtract the second term from the first term to find the common difference. In this case: $ 750,000 - 850,000 = -100,000 $, so each term decreases by 100,000.

Q: How many terms should I continue the sequence?

Look at what the question asks for. Usually it's three more terms like in this problem. Always read carefully to see exactly how many terms you need to find.

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

Focus on the pattern, not the size! Whether it's 85, 75 or 850,000, 750,000 - the difference method works the same way. You can even practice with smaller numbers first.

Arithmetic Sequences with Large Numbers

Complete the sequence:

$850{,}000,\ 750{,}000, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$850{,}000,\ 750{,}000, \ \ldots$

Step-by-step solution

Let's determine the sequence by following these steps:

Step 1: Identify the common difference by subtracting the second term from the first term: $750,000 - 850,000 = -100,000$ .
Step 2: Recognize that the sequence progresses by subtracting 100,000 from each term to get the next term.
Step 3: Apply the difference to find the next terms:

Third term: $650,000 = 750,000 - 100,000$
Fourth term: $550,000 = 650,000 - 100,000$
Fifth term: $450,000 = 550,000 - 100,000$

Therefore, the completed sequence following the same pattern is $650,000, 550,000, 450,000$ .

Given the choices, this corresponds to choice 1.

Final Answer

$650{,}000,\ 550{,}000, \ 450{,}000$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Calculate $750,000 - 850,000 = -100,000$ difference
Check: Verify each term decreases by exactly 100,000 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes or using inconsistent differences
Don't assume the difference changes between terms or use different amounts like -50,000 then -150,000 = wrong sequence! Arithmetic sequences have the same constant difference throughout. Always use the same common difference for every step in the sequence.

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 find the pattern when only two terms are given?

Subtract the second term from the first term to find the common difference. In this case: $750,000 - 850,000 = -100,000$ , so each term decreases by 100,000.

What if the numbers are getting smaller - is that still a sequence?

Yes! When numbers decrease by the same amount each time, it's called an arithmetic sequence with a negative common difference. The pattern is just as valid as increasing sequences.

How many terms should I continue the sequence?

Look at what the question asks for. Usually it's three more terms like in this problem. Always read carefully to see exactly how many terms you need to find.

Can I double-check my answer?

Absolutely! Make sure each consecutive pair has the same difference: $650,000 - 750,000 = -100,000$ and $550,000 - 650,000 = -100,000$ . Same difference = correct pattern!

What if I get confused with the large numbers?

Focus on the pattern, not the size! Whether it's 85, 75 or 850,000, 750,000 - the difference method works the same way. You can even practice with smaller numbers first.

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