Geometric Pattern Sequence: Identifying the Fifth Shape Element

Q: How do I know when a pattern repeats?

Look for the smallest group of shapes that keeps repeating. In this sequence, triangle-rectangle alternates every 2 positions, so the pattern length is 2.

Q: How do I find what shape is in position 10 or 20?

Divide the position number by the pattern length. The remainder tells you which shape in the pattern it matches. If remainder is 0, it's the last shape in the pattern.

Q: Can patterns have more than just 2 different shapes?

Absolutely! Patterns can include 3, 4, or more different shapes in various arrangements. The key is finding the repeating sequence.

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

Write out the sequence: Triangle, Rectangle, Triangle, Rectangle... Seeing it written helps identify the alternating pattern more easily.

Pattern Recognition with Alternating Shapes

Which shape appears in the fifth element of the sequence?

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Step-by-step video solution

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00:00 Find the next shape in the sequence

00:03 Let's identify the pattern

00:08 Triangle for each odd member

00:13 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Which shape appears in the fifth element of the sequence?

Final Answer

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Triangle and rectangle alternate in repeating sequence
Technique: Count positions: 1st triangle, 2nd rectangle, 3rd triangle, 4th rectangle
Check: Verify pattern continues: position 5 = triangle like positions 1 and 3 ✓

Common Mistakes

Avoid these frequent errors

Not identifying the complete repeating pattern
Don't just look at the first two shapes and assume that's the whole pattern = missing the alternating cycle! This leads to wrong predictions for later positions. Always identify the complete repeating unit before determining any position.

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 know when a pattern repeats?

Look for the smallest group of shapes that keeps repeating. In this sequence, triangle-rectangle alternates every 2 positions, so the pattern length is 2.

What if the pattern is longer than 2 shapes?

Some patterns repeat every 3, 4, or more positions! Always examine all given shapes to find the complete repeating unit before making predictions.

How do I find what shape is in position 10 or 20?

Divide the position number by the pattern length. The remainder tells you which shape in the pattern it matches. If remainder is 0, it's the last shape in the pattern.

Can patterns have more than just 2 different shapes?

Absolutely! Patterns can include 3, 4, or more different shapes in various arrangements. The key is finding the repeating sequence.

What if I can't see the pattern clearly?

Write out the sequence: Triangle, Rectangle, Triangle, Rectangle... Seeing it written helps identify the alternating pattern more easily.

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