Determine the Next Number in the 582,985 and 583,985 Sequence

Q: How do I know what number to add each time?

Always subtract the first number from the second number in the sequence. In this case: $ 583,985 - 582,985 = 1,000 $, so you add 1,000 each time.

Q: What if the numbers are really big like these?

Big numbers work exactly the same way! Focus on the difference between them, not their size. The pattern is what matters, not how large the numbers are.

Q: Could the sequence go down instead of up?

Yes! If the second number is smaller than the first, you'd subtract the same amount each time. Always check which direction the pattern goes.

Q: How many numbers should I find in the sequence?

Look at what the question asks for! Usually it wants the next 3 numbers after the given ones. Keep adding the common difference until you have enough.

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

Focus on the numerical value, not the commas. $ 582,985 $ is just 582985. The commas help us read it, but don't affect the math.

Arithmetic Sequences with Large Number Increments

Complete the sequence:

$582{,}985,\ 583{,}985, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$582{,}985,\ 583{,}985, \ \ldots$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the increment between the given sequence numbers.
Step 2: Use this increment to find the next numbers in the sequence.

Let's work through each step:

Step 1: Identify the increment.
The sequence begins with $582,985$ and $583,985$ . Calculate the difference between these numbers:
$583,985 - 582,985 = 1,000$ .
Thus, each number in the sequence increases by 1,000.

Step 2: Extend the sequence.
Starting from the last given number $583,985$ , add 1,000 to find the subsequent numbers:

The next number is $583,985 + 1,000 = 584,985$ .
The following number is $584,985 + 1,000 = 585,985$ .
Continue this process: $585,985 + 1,000 = 586,985$ .

Therefore, by continuing the arithmetic pattern, the completed sequence is:
$584,985, 585,985, 586,985$ .

Matching this result with the given choices, the correct answer is choice 3, which is:
$584,985, 585,985, 586,985$ .

Final Answer

$584{,}985,\ 585{,}985, \ 586{,}985$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Subtract first from second: $583,985 - 582,985 = 1,000$
Check: Each new term equals previous term plus 1,000 ✓

Common Mistakes

Avoid these frequent errors

Adding a small increment like 1 or 10
Don't assume the pattern increases by 1 or 10 just because it's a sequence = wrong numbers! This ignores the actual difference calculation. Always subtract the first term from the second term to find the true increment.

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 what number to add each time?

Always subtract the first number from the second number in the sequence. In this case: $583,985 - 582,985 = 1,000$ , so you add 1,000 each time.

What if the numbers are really big like these?

Big numbers work exactly the same way! Focus on the difference between them, not their size. The pattern is what matters, not how large the numbers are.

Could the sequence go down instead of up?

Yes! If the second number is smaller than the first, you'd subtract the same amount each time. Always check which direction the pattern goes.

How many numbers should I find in the sequence?

Look at what the question asks for! Usually it wants the next 3 numbers after the given ones. Keep adding the common difference until you have enough.

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

Focus on the numerical value, not the commas. $582,985$ is just 582985. The commas help us read it, but don't affect the math.

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