Subjects algebra

Sequence Increasing Decreasing D90553

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem asks us to determine whether the sequence \(a_n\) is increasing or decreasing by comparing \(a_{n+1}\) and \(a_n\). 2. To analyze this, we use the rule: - If \(a_{n+1} > a_n\), the sequence is increasing. - If \(a_{n+1} < a_n\), the sequence is decreasing. 3. Since the explicit formula for \(a_n\) is not given, the general approach is to find the expression for \(a_{n+1} - a_n\). 4. Calculate \(a_{n+1} - a_n\) and simplify it. 5. If \(a_{n+1} - a_n > 0\) for all relevant \(n\), the sequence is increasing. 6. If \(a_{n+1} - a_n < 0\) for all relevant \(n\), the sequence is decreasing. 7. Without the explicit formula for \(a_n\), we cannot determine the sign of \(a_{n+1} - a_n\). 8. Please provide the formula or terms of the sequence \(a_n\) to proceed with the comparison.