Complete Group C: Unravel the Sequence Pattern

Q: How do I find the pattern when the differences aren't the same?

Look for patterns in the differences themselves! In this problem, boys increase by 4, then 8, then 4, then 4 - there's still a pattern even when differences vary.

Q: Why do the boys and girls have different patterns?

Each sequence follows its own rule! Boys have an increasing sequence with alternating differences, while girls have a decreasing sequence. Always analyze each column separately.

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

Write out the differences step by step: $ 9-5=4 $, $ 17-9=8 $, etc. Sometimes patterns become clear when you see them listed in order.

Q: How do I know which direction the pattern continues?

Look at the given values around the missing term. Group C is between B (9 boys) and D (17 boys), so the missing value should fit logically between them.

Sequence Patterns with Alternating Differences

A sequence represents the division of boys and girls into groups and is structured according to a term-to-term rule.

Complete group C.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's complete group C together.

00:12 First, find the difference between all the girls' groups.

00:22 Next, calculate the difference from group B to group C.

00:27 This will give us the number of girls in group C.

00:35 Now, use the same steps to figure out how many boys are in group C.

00:41 Find the difference between all the boys' groups.

00:46 Then, calculate the difference from group B to group C.

00:51 This is the number of boys in group C.

00:55 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A sequence represents the division of boys and girls into groups and is structured according to a term-to-term rule.

Complete group C.

Step-by-step solution

To solve this problem, we need to recognize the patterns for both boys and girls across the groups:

For the boys: The sequence given is 5, 9, 17, 21, 25 for groups A, B, D, E, F respectively. Observing the differences: $9 - 5 = 4$ , $17 - 9 = 8$ , $21 - 17 = 4$ , $25 - 21 = 4$ . This means the sequence is increasing by alternating values of 4 and 8. Thus, the missing number for group C (after 9) should be $9 + 8 = 17$ .
For the girls: The sequence given is 25, 21, 13, 9, 5. Observing the differences: $21 - 25 = -4$ , $13 - 21 = -8$ , $9 - 13 = -4$ , $5 - 9 = -4$ . This means the sequence is decreasing by alternating values of -4 and -8. Thus, the missing number for group C (after 21) should be $21 - 8 = 13$ .

Therefore, the values for group C are:

13, 17

Final Answer

13, 17

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify alternating differences between consecutive terms in sequences
Technique: Boys: 4,8,4,4 pattern gives 9+4=13 for group C
Check: Verify both sequences maintain their alternating difference patterns ✓

Common Mistakes

Avoid these frequent errors

Assuming constant differences throughout the sequence
Don't add the same difference to every term = missing the alternating pattern! This creates wrong predictions because the sequence changes by different amounts. Always look for patterns in the differences themselves, not just single constant differences.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

How do I find the pattern when the differences aren't the same?

Look for patterns in the differences themselves! In this problem, boys increase by 4, then 8, then 4, then 4 - there's still a pattern even when differences vary.

Why do the boys and girls have different patterns?

Each sequence follows its own rule! Boys have an increasing sequence with alternating differences, while girls have a decreasing sequence. Always analyze each column separately.

What if I can't see the pattern in the differences?

Write out the differences step by step: $9-5=4$ , $17-9=8$ , etc. Sometimes patterns become clear when you see them listed in order.

How do I know which direction the pattern continues?

Look at the given values around the missing term. Group C is between B (9 boys) and D (17 boys), so the missing value should fit logically between them.

Can sequence patterns be more complex than this?

Yes! Some sequences have patterns like doubling, squaring, or even more complex rules. Always start by checking simple arithmetic differences first, then look for other patterns if needed.

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