Algebraic Expression: Converting Circular Pattern Sequences to n-term Formula

Q: How do I figure out if it's 6-n or something else?

Start by counting the circles in each figure! First figure = 5, second = 4, third = 3. Notice it decreases by 1 each time, so try $ 6-n $: when n=1, you get 6-1=5 ✓

Q: What if I can't see the pattern clearly?

Make a table! Write down figure number and number of circles side by side. Look for how the circles change as the figure number increases - does it go up, down, or stay the same?

Q: Why is it 6-n and not 5-n?

Test both formulas! For the first figure (n=1): $ 5-1 = 4 $ circles (wrong!) vs $ 6-1 = 5 $ circles (correct!). The formula must work for all figures.

Q: How do I know when to use subtraction vs addition?

Look at the direction of change! If circles decrease as figure numbers increase, use subtraction. If circles increase, use addition. The pattern here goes 5→4→3, so it's decreasing.

Q: What does the 'n' represent in these problems?

The variable n represents the position number of each figure in the sequence. So n=1 is the first figure, n=2 is the second figure, and so on.

Pattern Recognition with Decreasing Sequences

Choose the algebraic expression that corresponds to the number of circles in terms of n.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the sequence formula

00:03 Let's observe the number of circles in the first term

00:14 Let's observe the number of circles in the following terms

00:34 Let's substitute the first term in the equation and solve

00:38 We can see that this formula fits our sequence

00:42 Let's use the same method and check all suggested formulas

00:46 This formula doesn't fit our sequence

00:55 This formula doesn't fit either

01:02 And this one doesn't fit either

01:05 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the algebraic expression that corresponds to the number of circles in terms of n.

Final Answer

$6-n$

Key Points to Remember

Essential concepts to master this topic

Pattern Analysis: Count circles in each figure to identify the sequence
Technique: First figure has 5 circles, second has 4, third has 3
Check: Verify formula works: when n=1, 6-1=5 circles ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern increases instead of decreases
Don't assume n+1 or similar increasing formulas = wrong direction! The circles actually decrease from left to right (5, 4, 3, 2...). Always count carefully and check if the sequence goes up or down.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

How do I figure out if it's 6-n or something else?

Start by counting the circles in each figure! First figure = 5, second = 4, third = 3. Notice it decreases by 1 each time, so try $6-n$ : when n=1, you get 6-1=5 ✓

What if I can't see the pattern clearly?

Make a table! Write down figure number and number of circles side by side. Look for how the circles change as the figure number increases - does it go up, down, or stay the same?

Why is it 6-n and not 5-n?

Test both formulas! For the first figure (n=1): $5-1 = 4$ circles (wrong!) vs $6-1 = 5$ circles (correct!). The formula must work for all figures.

How do I know when to use subtraction vs addition?

Look at the direction of change! If circles decrease as figure numbers increase, use subtraction. If circles increase, use addition. The pattern here goes 5→4→3, so it's decreasing.

What does the 'n' represent in these problems?

The variable n represents the position number of each figure in the sequence. So n=1 is the first figure, n=2 is the second figure, and so on.

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