Complete the Number Sequence: Finding Missing Terms in 25, 21, 19, ...

Q: How do I find the common difference when terms are missing?

Use the two consecutive known terms you have! In this case, subtract 19 from 21 to get the common difference of $ -2 $.

Q: What if I can't tell if the sequence is increasing or decreasing?

Look at your known consecutive terms! Since $ 21 > 19 $ and 21 comes before 19, the sequence is decreasing by 2 each time.

Q: Can I work backwards from 25 to fill in the gaps?

Absolutely! Once you know the common difference is $ -2 $, you can work backwards: $ 25 - 2 = 23 $, then forwards: $ 19 - 2 = 17 $, $ 17 - 2 = 15 $.

Arithmetic Sequences with Missing Terms

Complete the following sequence:

$25,\ldots,21,19,\ldots,\ldots$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following sequence:

$25,\ldots,21,19,\ldots,\ldots$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Determine the common difference by looking at the known terms, 21 and 19.
Step 2: Apply the common difference to find the missing terms in the sequence.
Step 3: Verify the sequence pattern to ensure accuracy.

Now, let's work through each step:

Step 1: The common difference between 21 and 19 is 2. Thus, each number in the sequence is reduced by 2 from the previous one.

Step 2: Starting from 25, subtract 2 to fill in the first gap: $25 - 2 = 23$ . Now the sequence is 25, 23, ..., 21, 19.

From 19, subtract 2 to fill in the next gap: $19 - 2 = 17$ , then $17 - 2 = 15$ . Thus, the complete sequence is:

$25, 23, 21, 19, 17, 15$

Therefore, the solution to the problem is $25, 23, 21, 19, 17, 15$ .

Final Answer

$25,23,21,19,17,15$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common difference by subtracting consecutive known terms
Technique: Apply common difference backwards and forwards: 21 - 19 = -2
Check: Verify each term differs by same amount: 25→23→21→19→17→15 ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern continues in the wrong direction
Don't think 25, 21, 19 means adding different amounts each time = random guessing! The sequence has one constant difference throughout. Always find the common difference first, then apply it consistently in both directions.

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 find the common difference when terms are missing?

Use the two consecutive known terms you have! In this case, subtract 19 from 21 to get the common difference of $-2$ .

What if I can't tell if the sequence is increasing or decreasing?

Look at your known consecutive terms! Since $21 > 19$ and 21 comes before 19, the sequence is decreasing by 2 each time.

Can I work backwards from 25 to fill in the gaps?

Absolutely! Once you know the common difference is $-2$ , you can work backwards: $25 - 2 = 23$ , then forwards: $19 - 2 = 17$ , $17 - 2 = 15$ .

How do I know I have the right number of terms?

Count the gaps in the original sequence and make sure your answer has the same number of terms. The original shows 6 positions, so your complete sequence should have exactly 6 numbers.

What if my common difference comes out as a fraction or decimal?

That's perfectly fine! Arithmetic sequences can have any constant difference. Just apply the same fractional or decimal difference to each step consistently.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Magnitude up to 100 questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime