Complete the Arithmetic Sequence: 20, 30, 40...

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

Look at the difference between consecutive terms! In this sequence, $ 30 - 20 = 10 $ and $ 40 - 30 = 10 $, so you always add 10.

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

Then it's not an arithmetic sequence! Arithmetic sequences must have the same difference between all consecutive terms. If differences vary, it might be a different type of pattern.

Q: Can arithmetic sequences go backwards?

Absolutely! If the common difference is negative, the sequence decreases. For example: 50, 40, 30, 20... has a common difference of -10.

Q: What's the formula for the nth term?

For arithmetic sequences, use: $ a_n = a_1 + (n-1)d $Where $ a_1 $ is the first term and $ d $ is the common difference.

Arithmetic Sequences with Constant Differences

Complete the sequence:

$20,30,40\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$20,30,40\ldots$

Step-by-step solution

To complete the sequence $20, 30, 40, \ldots$ , we need to determine the pattern.

Identify the pattern: Find the difference between successive terms.
Calculate the difference: $30 - 20 = 10$ and $40 - 30 = 10$ . The common difference is 10.
Continue the sequence using this pattern: Add 10 to the last given number to find the next number.
Extend the sequence:

The term after 40 is $40 + 10 = 50$ .
The next term is $50 + 10 = 60$ .
The next term is $60 + 10 = 70$ .

Thus, the complete sequence is $20, 30, 40, 50, 60, 70$ .

Therefore, the solution to the problem is $20, 30, 40, 50, 60, 70$ , corresponding to choice 4.

Final Answer

$20,30,40,50,60,70$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Calculate differences: $30 - 20 = 10$ , $40 - 30 = 10$
Check: Verify each term follows the pattern: $20 + 10 = 30$ , $30 + 10 = 40$ ✓

Common Mistakes

Avoid these frequent errors

Adding random numbers without finding the pattern
Don't just add any number like 1 or 5 to continue the sequence = completely wrong terms! This ignores the established pattern and gives nonsensical results. Always find the common difference first by subtracting consecutive terms.

Practice Quiz

Test your knowledge with interactive questions

Complete the following sequence:

$20,\ldots,24,26\ldots ,\ldots$

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, $30 - 20 = 10$ and $40 - 30 = 10$ , so you always add 10.

What if the differences aren't the same?

Then it's not an arithmetic sequence! Arithmetic sequences must have the same difference between all consecutive terms. If differences vary, it might be a different type of pattern.

Can arithmetic sequences go backwards?

Absolutely! If the common difference is negative, the sequence decreases. For example: 50, 40, 30, 20... has a common difference of -10.

How many terms should I find to complete the sequence?

Check what the question asks for! Some want 3 more terms, others want 6 total terms. In this problem, we needed to match one of the given answer choices.

What's the formula for the nth term?

For arithmetic sequences, use: $a_n = a_1 + (n-1)d$
Where $a_1$ is the first term and $d$ is the common difference.

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