Find the Missing Numbers: 15, 22, 29, _, 43, 50, _, _

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

Use the known consecutive terms first! In this sequence, calculate $22 - 15 = 7$ and $29 - 22 = 7$. The common difference is 7.

Q: What if the differences I calculate don't match?

If differences between known terms aren't equal, it's not an arithmetic sequence. Double-check your calculations first, then look for other patterns like geometric sequences or quadratic patterns.

Q: Can I work backwards from 43 to find the missing term?

Absolutely! Since $43 - 7 = 36$, you get the same answer. Working both forwards and backwards is a great way to double-check your work.

Arithmetic Sequences with Multiple Missing Terms

Given a series that is missing some terms.

15 , 22 , 29 , _ , 43 , 50 , _ , _

What is the missing set of numbers?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the missing terms

00:04 Find the difference between each consecutive term

00:12 This is the pattern of the sequence

00:17 Calculate the missing terms according to the pattern we found

00:25 When going in this direction, we need to add 7 from the known term

00:36 Calculate the missing terms

00:44 Use the same method

00:52 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

Given a series that is missing some terms.

15 , 22 , 29 , _ , 43 , 50 , _ , _

What is the missing set of numbers?

Step-by-step solution

Let's solve the problem step-by-step:

Step 1: Calculate the common difference
The difference between 22 and 15 is $22 - 15 = 7$ .
The difference between 29 and 22 is $29 - 22 = 7$ .
The difference between 43 and the next term should be 7, therefore it needs confirmation.
Step 2: Determine the pattern
Since the differences between the consecutive terms (15, 22, 29) and (unknown, 43, 50) are consistent, the sequence has a common difference of 7.
Step 3: Calculate the missing terms using the common difference
- The term after 29 is $29 + 7 = 36$ .
- After 43, there must be 50, validating that $43 + 7 = 50$ .
- The term after 50 can be found by adding 7 again: $50 + 7 = 57$ .
- Add 7 once more to find the final missing term: $57 + 7 = 64$ .

Therefore, the missing numbers in the sequence are 36, 57, and 64. These fill in the blanks and maintain the arithmetic progression.

The correct set of missing numbers is 36, 57, 64

Final Answer

36, 57, 64

Key Points to Remember

Essential concepts to master this topic

Pattern: Find common difference between consecutive known terms first
Technique: Add common difference 7: 29 + 7 = 36
Check: Verify pattern works throughout: 15, 22, 29, 36, 43, 50, 57, 64 ✓

Common Mistakes

Avoid these frequent errors

Guessing missing numbers without finding the pattern
Don't just guess numbers that 'look right' = random wrong answers! This ignores the mathematical relationship between terms. Always find the common difference first by subtracting consecutive known terms.

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 find the common difference when terms are missing?

Use the known consecutive terms first! In this sequence, calculate $22 - 15 = 7$ and $29 - 22 = 7$ . The common difference is 7.

What if the differences I calculate don't match?

If differences between known terms aren't equal, it's not an arithmetic sequence. Double-check your calculations first, then look for other patterns like geometric sequences or quadratic patterns.

How can I check if my missing numbers are correct?

Substitute your answers back into the sequence and verify the common difference of 7 appears between every consecutive pair of terms throughout the entire sequence.

Can I work backwards from 43 to find the missing term?

Absolutely! Since $43 - 7 = 36$ , you get the same answer. Working both forwards and backwards is a great way to double-check your work.

What if there were more missing terms at the end?

Just keep adding the common difference! After 64, the next terms would be $64 + 7 = 71$ , then $71 + 7 = 78$ , and so on.

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