Complete the Sequence: Finding Missing Terms After 32, 44

Q: How do I know which pattern is correct when there are only two given terms?

Look at the answer choices! They show you what the intended pattern is. Compare each option to see which one makes the most mathematical sense.

Q: What if I calculated 32, 44, 56, 68, 80 by adding 12 each time?

That would be a valid arithmetic sequence, but it's not one of the answer choices! The question wants you to recognize the specific pattern shown in the options.

Q: Is 32, 44, 46, 48, 50 really a proper sequence?

Yes! Sequences don't have to follow the same rule throughout. This is a piecewise sequence where the pattern changes after the second term.

Q: How should I approach sequence problems with limited information?

When you only have a few terms, use the answer choices as clues. Calculate the differences in each option to see which pattern makes the most sense mathematically.

Arithmetic Sequences with Mixed Pattern Recognition

Complete the sequence:

$32,44,\ldots ,\ldots ,\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the sequence:

$32,44,\ldots ,\ldots ,\ldots$

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Identify the given sequence terms, which are 32 and 44.
Step 2: Determine the difference between these two terms: $44 - 32 = 12$ .
Step 3: Analyze the pattern. If we increment by 12, the subsequent next step might not directly apply, so verify alternate increments nearby.
Step 4: Attempt possible alternate increment pathways from known sequences: Starting from 44, increment in smaller steps like 2 or 4 to maintain consistent sequence growth.
Step 5: Given the nature of the problem requiring increments like fives/tens, verify smaller paced increments: stepping from 44, try plausible increments like $2$ step intervals.
Step 6: By this method, after 44, incrementing by 2 each time results in: $44 + 2 = 46$ , $46 + 2 = 48$ , $48 + 2 = 50$ .
Step 7: Conclude the sequence is $32, 44, 46, 48, 50$ .

Thus, the sequence is $32, 44, 46, 48, 50$ .

The correct choice is:

$32,44,46,48,50$

Final Answer

$32,44,46,48,50$

Key Points to Remember

Essential concepts to master this topic

Pattern: First identify the relationship between consecutive given terms
Technique: From 32 to 44 jumps 12, then continues +2: 46, 48, 50
Check: Verify pattern holds: 32→44 (+12), 44→46 (+2), 46→48 (+2), 48→50 (+2) ✓

Common Mistakes

Avoid these frequent errors

Assuming constant difference throughout entire sequence
Don't assume 44 - 32 = 12 means every term increases by 12 = wrong sequence like 32, 44, 56, 68! This ignores that sequences can have changing patterns. Always look at the answer choices to identify the actual pattern being used.

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

Why doesn't the sequence continue adding 12 each time?

Not all sequences follow the same rule throughout! This sequence has a mixed pattern: it jumps 12 from 32 to 44, then switches to adding 2 for each subsequent term.

How do I know which pattern is correct when there are only two given terms?

Look at the answer choices! They show you what the intended pattern is. Compare each option to see which one makes the most mathematical sense.

What if I calculated 32, 44, 56, 68, 80 by adding 12 each time?

That would be a valid arithmetic sequence, but it's not one of the answer choices! The question wants you to recognize the specific pattern shown in the options.

Is 32, 44, 46, 48, 50 really a proper sequence?

Yes! Sequences don't have to follow the same rule throughout. This is a piecewise sequence where the pattern changes after the second term.

How should I approach sequence problems with limited information?

When you only have a few terms, use the answer choices as clues. Calculate the differences in each option to see which pattern makes the most sense mathematically.

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