The given sequence is: 1, 4, 9, 17, 29.

Let's identify the pattern by examining the differences between consecutive terms:

• $4 - 1 = 3$
• $9 - 4 = 5$
• $17 - 9 = 8$
• $29 - 17 = 12$

The differences between consecutive terms are: 3, 5, 8, 12.

Now, let's look at the differences between these differences:

• $5 - 3 = 2$
• $8 - 5 = 3$
• $12 - 8 = 4$

The second differences are increasing by 1. This indicates that the sequence follows a quadratic pattern.

Finding the next terms:

• The next difference should be $12 + 5 = 17$.

• Adding this to the last term: $29 + 17 = 46$.

• The next difference should be $17 + 6 = 23$.

• Adding this: $46 + 23 = 69$.

• The next difference should be $23 + 7 = 30$.

• Adding this: $69 + 30 = 99$.

Thus, the sixth, seventh, and eighth terms are:

• Sixth term = 46
• Seventh term = 69
• Eighth term = 99

Would you like further details or have any questions?

Here are 5 related questions:

1. How can you find the nth term of a quadratic sequence?
2. What are the first and second differences in a sequence?
3. How do you derive a general formula for a quadratic sequence?
4. What are some real-world applications of quadratic sequences?
5. How do linear and quadratic sequences differ in terms of growth?

Tip: To identify quadratic sequences, always check for constant second differences!