Complete the Arithmetic Sequence: Finding Missing Numbers After 15

Q: How do I find the pattern in a sequence?

Look at the difference between consecutive terms. In this sequence: $ 3-(-3)=6 $, $ 9-3=6 $, $ 15-9=6 $. Since all differences equal 6, that's your pattern!

Q: What if the differences aren't the same?

If differences vary, it might be a geometric sequence (multiply/divide pattern) or another type. For arithmetic sequences, differences must be constant.

Q: Can arithmetic sequences have negative numbers?

Absolutely! This sequence starts with $ -3 $ and still follows the same addition rule. Negative numbers don't change how arithmetic sequences work.

Q: How many terms should I find to be sure of the pattern?

Check at least 3 consecutive differences to confirm the pattern. In this problem, we have 4 given terms, so we can verify the pattern with 3 differences before continuing.

Q: What if I calculated the wrong common difference?

Always double-check by calculating differences between all consecutive pairs. If you get different values, recalculate carefully, especially with negative numbers.

Arithmetic Sequences with Constant Differences

Fill in the missing numbers

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Understand the problem

Fill in the missing numbers

Step-by-step solution

Let's look at the numbers from left to right:

$-3,3,9,15$

We notice that the common operation is:

$+6$

$-3+6=3$

$3+6=9$

$9+6=15$

Therefore, the next sequence will be:

$15+6=21$

$21+6=27$

Final Answer

27, 21

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Add the common difference: $15 + 6 = 21$ , $21 + 6 = 27$
Verification: Check that differences are consistent: $3-(-3) = 6$ , $9-3 = 6$ , $15-9 = 6$ ✓

Common Mistakes

Avoid these frequent errors

Finding differences incorrectly or inconsistently
Don't calculate $3-(-3) = 0$ or skip checking all differences = wrong pattern identification! This leads to continuing with the wrong common difference. Always subtract each term from the next term in order and verify all differences are equal.

Practice Quiz

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All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

How do I find the pattern in a sequence?

Look at the difference between consecutive terms. In this sequence: $3-(-3)=6$ , $9-3=6$ , $15-9=6$ . Since all differences equal 6, that's your pattern!

What if the differences aren't the same?

If differences vary, it might be a geometric sequence (multiply/divide pattern) or another type. For arithmetic sequences, differences must be constant.

Can arithmetic sequences have negative numbers?

Absolutely! This sequence starts with $-3$ and still follows the same addition rule. Negative numbers don't change how arithmetic sequences work.

How many terms should I find to be sure of the pattern?

Check at least 3 consecutive differences to confirm the pattern. In this problem, we have 4 given terms, so we can verify the pattern with 3 differences before continuing.

What if I calculated the wrong common difference?

Always double-check by calculating differences between all consecutive pairs. If you get different values, recalculate carefully, especially with negative numbers.

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