Predict the Next Number: Understanding the Pattern in 57,000, 58,000, 59,000...

Q: How do I know if it's really adding 1,000 each time?

Calculate the difference between each pair of consecutive terms. In this sequence: 58,000 - 57,000 = 1,000 and 59,000 - 58,000 = 1,000. Since both differences are the same, the pattern is consistent!

Arithmetic Sequences with Large Numbers

Complete the sequence:

$57{,}000,\ 58{,}000,\ 59{,}000, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$57{,}000,\ 58{,}000,\ 59{,}000, \ \ldots$

Step-by-step solution

To solve this problem, we'll analyze the pattern of the given sequence:

Step 1: Identify the pattern in the sequence.
Step 2: Calculate the common difference.
Step 3: Apply this pattern to find the next numbers.

Step 1: Examine the given sequence: $57,000, 58,000, 59,000$ .

Step 2: The difference between consecutive terms is $58,000 - 57,000 = 1,000$ and $59,000 - 58,000 = 1,000$ . Therefore, the common difference is $1,000$ .

Step 3: To find the next terms, add $1,000$ to the last term:

Add $1,000$ to $59,000$ to get $60,000$ .
Add $1,000$ to $60,000$ to get $61,000$ .
Add $1,000$ to $61,000$ to get $62,000$ .

Thus, the complete sequence is: $60,000, 61,000, 62,000$ .

Therefore, the solution to the problem is: $60,000, 61,000, 62,000$ .

Final Answer

$60{,}000,\ 61{,}000,\ 62{,}000$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Look for the constant difference between consecutive terms
Technique: Calculate common difference: 58,000 - 57,000 = 1,000
Check: Verify each term increases by the same amount: 1,000 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes based on digit position
Don't focus only on the changing digits (57, 58, 59) and assume the pattern becomes 59.1, 59.2 = wrong sequence! This ignores the actual numerical difference. Always calculate the exact difference between consecutive terms to find the true pattern.

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 it's really adding 1,000 each time?

Calculate the difference between each pair of consecutive terms. In this sequence: 58,000 - 57,000 = 1,000 and 59,000 - 58,000 = 1,000. Since both differences are the same, the pattern is consistent!

What if I see a different pattern like 60,000, 70,000, 80,000?

That would mean the common difference is 10,000, not 1,000! Always check your pattern against the given terms. Since 57,000 to 58,000 is only 1,000, the 10,000 pattern doesn't match.

Why can't the next numbers be 59,001, 59,002, 59,003?

That pattern adds only 1 each time, but our sequence adds 1,000 each time. The difference between 57,000 and 58,000 is 1,000, not 1. Always maintain the same common difference throughout!

How many terms should I predict in the sequence?

The question shows three given terms, so typically predict the next three terms. This gives enough examples to demonstrate you understand the pattern: 60,000, 61,000, 62,000.

What if I make an arithmetic error in my calculations?

Double-check your addition! For example: 59,000 + 1,000 = 60,000, then 60,000 + 1,000 = 61,000. You can also verify by checking that each new term is exactly 1,000 more than the previous one.

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