Complete the Arithmetic Sequence: Finding Missing Terms in 60, 50, ..., 30

Q: How do I know this is an arithmetic sequence?

Look for a constant difference between consecutive terms! Since $ 60 - 50 = 10 $, we expect the same difference throughout the sequence.

Q: Can I work backwards from 30 to find the missing term?

Absolutely! If the common difference is -10, then the term before 30 must be $ 30 + 10 = 40 $. This confirms our pattern!

Q: What if there are multiple missing terms?

Use the same method: find the common difference, then add or subtract it step by step. Each term = previous term + common difference.

Q: How can I check if my complete sequence is correct?

Verify that every consecutive pair has the same difference: 60-50=-10, 50-40=-10, 40-30=-10, etc. If all differences match, you're right!

Arithmetic Sequences with Missing Terms

Complete the sequence:

$60,50,\ldots30,\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$60,50,\ldots30,\ldots$

Step-by-step solution

To solve this problem, we will identify and use the pattern within the given sequence:

Step 1: Start with the given numbers $60$ and $50$ .
Step 2: Calculate the difference between these two numbers. We have $60 - 50 = 10$ .
Step 3: Assume this difference will continue throughout the sequence. This assumption is necessary because it suggests a common arithmetic sequence structure.

Following these steps, we can complete the sequence:

First term is $60$ .

Second term is $50$ .

Based on the assumption of an arithmetic sequence with a common difference of $-10$ :

Third term: $50 - 10 = 40$ .

Fourth term: $40 - 10 = 30$ .

Continuing this pattern:
Fifth term: $30 - 10 = 20$ .
Sixth term: $20 - 10 = 10$ .

Therefore, the complete sequence is $60, 50, 40, 30, 20, 10$ .

Final Answer

$60,50,40,30,20,10$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find common difference between consecutive terms first
Technique: Calculate $60 - 50 = -10$ then subtract 10 repeatedly
Check: Verify each term follows the pattern: 40-10=30, 30-10=20 ✓

Common Mistakes

Avoid these frequent errors

Assuming random patterns without checking consistency
Don't guess patterns like +5, -15, +10 without verification = wrong sequence! This creates inconsistent differences that don't follow arithmetic sequence rules. Always find the common difference first and apply it consistently throughout.

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 this is an arithmetic sequence?

Look for a constant difference between consecutive terms! Since $60 - 50 = 10$ , we expect the same difference throughout the sequence.

What if the given terms don't follow a clear pattern?

Check if it's arithmetic (constant difference) or geometric (constant ratio). If neither works, look for other patterns like squares, cubes, or alternating sequences.

Can I work backwards from 30 to find the missing term?

Absolutely! If the common difference is -10, then the term before 30 must be $30 + 10 = 40$ . This confirms our pattern!

What if there are multiple missing terms?

Use the same method: find the common difference, then add or subtract it step by step. Each term = previous term + common difference.

How can I check if my complete sequence is correct?

Verify that every consecutive pair has the same difference: 60-50=-10, 50-40=-10, 40-30=-10, etc. If all differences match, you're right!

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