https://file.aiquickdraw.com/mathbot/file/1727609466899tqq25ldu.jpg

The image contains four mathematical expressions involving sequences \( u_n \) in terms of \( n \). I'll rewrite each of them below:

1. \( u_n = 3n^2 + 5n - 11 \)
2. \( u_n = -n^3 - 3n + \frac{1}{n^2} \)
3. \( u_n = (2 - 3n)(n^2 + 5) \)
4. \( u_n = \frac{5}{5 + 3n} \)

Would you like detailed solutions or explanations for each sequence? Let me know if you have any specific questions!

Here are some related questions to explore further:

1. What is the value of \( u_n \) for \( n = 1 \) in the first sequence?
2. How does the second sequence behave as \( n \) approaches infinity?
3. Can you simplify the third sequence by expanding the expression?
4. What happens to the fourth sequence as \( n \) becomes very large?
5. Can you calculate the derivative of any of these sequences with respect to \( n \)?

**Tip:** When dealing with sequences, always check for patterns or behaviors as \( n \) increases or decreases to understand long-term trends.

Solve the four mathematical sequence problems provided in the image.

Explore solutions to polynomial and rational sequence problems, including expressions like u_n = 3n^2 + 5n - 11 and u_n = -n^3 - 3n + 1/n^2. This page provides detailed step-by-step explanations suitable for Grades 10-12.

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