Complete the Number Sequence: Finding the Pattern Starting with 5, 7

Q: What if the sequence could follow multiple patterns?

With only two terms given, arithmetic sequences are the most common pattern tested. Calculate the difference between terms and apply it consistently unless told otherwise.

Q: How do I find the common difference?

Subtract the first term from the second term: $ d = a_2 - a_1 $. In this case, $ 7 - 5 = 2 $.

Q: What if the difference isn't a whole number?

That's fine! Common differences can be fractions, decimals, or even negative numbers. Just apply the same difference consistently throughout the sequence.

Q: Could this be a different type of sequence?

Yes, but arithmetic sequences (constant difference) are most common in basic problems. More advanced sequences include geometric (constant ratio) or other patterns, but start with arithmetic first.

Arithmetic Sequences with Common Difference

Complete the following sequence:

$5,7\ldots$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following sequence:

$5,7\ldots$

Step-by-step solution

To solve this problem, we'll identify whether the sequence follows a recognizable pattern. The sequence so far is $5, 7$ .

Let's determine whether it follows an arithmetic sequence:

First Term ( $a_1$ ) = 5
Second Term ( $a_2$ ) = 7
The Common Difference ( $d$ ) = $7 - 5 = 2$

Assuming a consistent common difference, the sequence appears to be an arithmetic sequence increasing every term by 2.

Let's calculate the next few terms:

Third Term ( $a_3$ ) = $7 + 2 = 9$
Fourth Term ( $a_4$ ) = $9 + 2 = 11$
Fifth Term ( $a_5$ ) = $11 + 2 = 13$

Thus, the full sequence is: $5, 7, 9, 11, 13$ .

A review of the multiple-choice options shows that the correct answer is given by choice 1: $5, 7, 9, 11, 13$ .

Therefore, the complete sequence is $5, 7, 9, 11, 13$ .

Final Answer

$5,7,9,11,13$

Key Points to Remember

Essential concepts to master this topic

Pattern Rule: Arithmetic sequences add the same value each time
Technique: Find difference: $7 - 5 = 2$ , then continue adding 2
Check: Verify pattern holds: $5+2=7, 7+2=9, 9+2=11, 11+2=13$ ✓

Common Mistakes

Avoid these frequent errors

Assuming patterns without checking differences
Don't just guess the next numbers randomly = wrong sequence! Students often pick numbers that "look right" without calculating the actual common difference. Always find the difference between consecutive terms first, then apply it consistently.

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

What if the sequence could follow multiple patterns?

With only two terms given, arithmetic sequences are the most common pattern tested. Calculate the difference between terms and apply it consistently unless told otherwise.

How do I find the common difference?

Subtract the first term from the second term: $d = a_2 - a_1$ . In this case, $7 - 5 = 2$ .

What if the difference isn't a whole number?

That's fine! Common differences can be fractions, decimals, or even negative numbers. Just apply the same difference consistently throughout the sequence.

How many terms should I find?

Look at the answer choices to see how many terms are expected. Usually it's 3-5 terms total for this type of problem.

Could this be a different type of sequence?

Yes, but arithmetic sequences (constant difference) are most common in basic problems. More advanced sequences include geometric (constant ratio) or other patterns, but start with arithmetic first.

What if my calculated terms don't match any answer choice?

Double-check your common difference calculation! Make sure you're subtracting correctly: second term minus first term. Then verify you're adding the same amount each time.

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