Complete the Arithmetic Sequence: 200, 300, 400...

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

Look at the difference between consecutive terms. In this sequence: $ 300 - 200 = 100 $ and $ 400 - 300 = 100 $. Since both differences are 100, you add 100 each time!

Q: What if the differences aren't the same?

If consecutive differences aren't equal, it's not an arithmetic sequence. Check your calculations again, or consider if it might be a different type of sequence like geometric or quadratic.

Q: Can arithmetic sequences decrease?

Absolutely! If each term is smaller than the previous one, you have a negative common difference. For example: 100, 80, 60, 40... has a common difference of -20.

Q: What's the difference between arithmetic and geometric sequences?

Arithmetic sequences add the same number each time (like +100). Geometric sequences multiply by the same number each time (like ×2). This problem adds 100, so it's arithmetic!

Arithmetic Sequences with Constant Differences

Complete the sequence:

$200,300,400\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$200,300,400\ldots$

Step-by-step solution

The sequence provided is $200, 300, 400, \ldots$ . To determine the pattern, calculate the difference between consecutive terms:

The difference between $300$ and $200$ is $100$ .
The difference between $400$ and $300$ is $100$ again.

This confirms the sequence increases by $100$ for each successive term. To extend this sequence:

Add $100$ to $400$ to get $500$ .
Add $100$ to $500$ to get $600$ .
Add $100$ to $600$ to get $700$ .

Thus, the sequence continued is: $200, 300, 400, 500, 600, 700$ .

The correct answer is:
$200,300,400,500,600,700$

Final Answer

$200,300,400,500,600,700$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: $300 - 200 = 100$ , so add 100 each time
Check: Verify the pattern holds: $400 + 100 = 500$ , $500 + 100 = 600$ ✓

Common Mistakes

Avoid these frequent errors

Adding 1 to each term instead of finding the common difference
Don't just add 1 to get 401, 402, 403 = wrong pattern! This ignores the actual difference between terms. Always calculate the difference between consecutive terms first, then apply that same difference consistently.

Practice Quiz

Test your knowledge with interactive questions

Complete the following sequence:

$1,3.\ldots$

FAQ

Everything you need to know about this question

How do I know what number to add each time?

Look at the difference between consecutive terms. In this sequence: $300 - 200 = 100$ and $400 - 300 = 100$ . Since both differences are 100, you add 100 each time!

What if the differences aren't the same?

If consecutive differences aren't equal, it's not an arithmetic sequence. Check your calculations again, or consider if it might be a different type of sequence like geometric or quadratic.

Can arithmetic sequences decrease?

Absolutely! If each term is smaller than the previous one, you have a negative common difference. For example: 100, 80, 60, 40... has a common difference of -20.

How many terms should I continue the sequence?

Follow the instructions in your problem. This question shows 6 terms total, so continue until you have the same number of terms as shown in the answer choices.

What's the difference between arithmetic and geometric sequences?

Arithmetic sequences add the same number each time (like +100). Geometric sequences multiply by the same number each time (like ×2). This problem adds 100, so it's arithmetic!

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