what is the fifth term in this series: 5; 2; 9; 6;

To find the fifth term in the sequence \( 5, 2, 9, 6 \), let's analyze the pattern.

We can observe the differences between consecutive terms:
- \( 5 \to 2 \) (difference of \(-3\))
- \( 2 \to 9 \) (difference of \(+7\))
- \( 9 \to 6 \) (difference of \(-3\))

This suggests that the differences alternate between \(-3\) and \(+7\).

If this pattern continues, the next difference should be \(+7\).

So, the fifth term is:
\[
6 + 7 = 13
\]

Thus, the fifth term in the series is \( 13 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general formula for arithmetic sequences?
2. How can you find the \( n \)-th term of a sequence?
3. What is the difference between arithmetic and geometric sequences?
4. How can you determine if a sequence is linear or quadratic?
5. What are some common types of patterns found in number sequences?

**Tip:** When identifying patterns in a sequence, always check the differences between terms. This helps determine if the sequence is arithmetic, geometric, or follows another rule.

What is the fifth term in this series: 5; 2; 9; 6?

Discover how to find the fifth term in the sequence 5, 2, 9, 6 by analyzing the pattern of differences between consecutive terms. A step-by-step guide suitable for students in Grades 5-7.

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