The given sequence is: 5, 0, 10, -5, 15, ?

Let's analyze the differences between consecutive terms:

1. \( 0 - 5 = -5 \)
2. \( 10 - 0 = 10 \)
3. \( -5 - 10 = -15 \)
4. \( 15 - (-5) = 20 \)

The differences are: -5, 10, -15, 20.

This sequence alternates between positive and negative differences, and the magnitude of the differences increases by 5 each time.

Following this pattern, the next difference should be \( -20 + 5 = 25 \) (positive, since the sequence alternates).

Adding this to the last term:

\( 15 + 25 = 40 \)

So, the next term in the sequence is **40**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What would be the 7th term of the sequence?
2. Can you find the 8th term of the sequence?
3. How can this sequence be represented graphically?
4. What is the general rule for forming the next term?
5. What are some other sequences with alternating differences?

**Tip:** For sequences with alternating positive and negative differences, focus on both the sign change and the pattern in the magnitude of the differences.

Discover the solution to the sequence problem 5, 0, 10, -5, 15, ? with step-by-step analysis. This problem involves recognizing the pattern in alternating differences and determining the next term. Suitable for students in Grades 7-9 interested in sequences and pattern recognition in mathematics.

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