Identify the Common Difference: Complete the Sequence of 3,000, 3,010, 3,020, ...

Q: What if I calculated the wrong common difference?

Double-check by calculating the difference between multiple pairs of consecutive terms. In our sequence: $3,010 - 3,000 = 10$ and $3,020 - 3,010 = 10$. Both should be the same!

Q: Can the common difference be negative?

Yes! If each term gets smaller, the common difference is negative. For example: 100, 95, 90... has a common difference of $-5$.

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

Don't worry about the size of the numbers! Focus on the pattern. Whether it's 3, 13, 23... or 3,000, 3,010, 3,020..., the method is exactly the same.

Arithmetic Sequences with Common Differences

Complete the sequence:

$3{,}000,\ 3{,}010,\ 3{,}020, \ \ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$3{,}000,\ 3{,}010,\ 3{,}020, \ \ldots$

Step-by-step solution

To solve this problem, we will identify the progression pattern in the given sequence of numbers:

Step 1: Examine the initial terms of the sequence 3,000, 3,010, 3,020.

Observe the difference between these terms:

$3,010 - 3,000 = 10$
$3,020 - 3,010 = 10$

The difference between consecutive terms is consistently 10. This indicates that the sequence increases by 10 with each new term.

Since the sequence is arithmetic and each term increases by 10, let's calculate the next few terms by adding 10 to the last given number, $3,020$ :

Next term: $3,020 + 10 = 3,030$
Following term: $3,030 + 10 = 3,040$
Final term required: $3,040 + 10 = 3,050$

Thus, the next three numbers in the sequence are $3,030$ , $3,040$ , and $3,050$ .

The choice that matches this sequence completion is option 2: $3,030,\ 3,040,\ 3,050$ .

Final Answer

$3{,}030,\ 3{,}040,\ 3{,}050$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the difference between consecutive terms first
Technique: Add common difference: 3,020 + 10 = 3,030
Check: Verify each new term increases by same amount: 10 ✓

Common Mistakes

Avoid these frequent errors

Adding different amounts to each term
Don't add 5 to the first term, then 10 to the next = inconsistent pattern! This creates a random sequence instead of an arithmetic one. Always add the same common difference to each consecutive term.

Practice Quiz

Test your knowledge with interactive questions

Complete the sequence:

$1{,}007,\ 1{,}008,\ 1{,}009, \ \ldots$

FAQ

Everything you need to know about this question

How do I find the common difference in an arithmetic sequence?

Subtract any term from the next term in the sequence. In this example: $3,010 - 3,000 = 10$ . The common difference is 10.

What if I calculated the wrong common difference?

Double-check by calculating the difference between multiple pairs of consecutive terms. In our sequence: $3,010 - 3,000 = 10$ and $3,020 - 3,010 = 10$ . Both should be the same!

Can the common difference be negative?

Yes! If each term gets smaller, the common difference is negative. For example: 100, 95, 90... has a common difference of $-5$ .

How many terms should I find to complete the sequence?

Look at the answer choices to see how many terms are needed. In this problem, each option shows three more terms, so find the next three numbers in the pattern.

What if the numbers are really large like these?

Don't worry about the size of the numbers! Focus on the pattern. Whether it's 3, 13, 23... or 3,000, 3,010, 3,020..., the method is exactly the same.

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