Find the limit of the sequence with the given \( n \)th term. \[ a_{n}=\cos \left(\frac{8}{n}\right) \]

To find the limit of the sequence \( a_n = \cos\left(\frac{8}{n}\right) \) as \( n \) approaches infinity, follow these steps: 1. **Analyze the Argument of the Cosine Function:** As \( n \) becomes very large, the term \( \frac{8}{n} \) becomes very small because dividing a constant by an increasingly large number results in a value that approaches zero. \[ \lim_{n \to \infty} \frac{8}{n} = 0 \] 2. **Apply the Continuity of the Cosine Function:** The cosine function is continuous, which means you can interchange the limit and the function. Therefore: \[ \lim_{n \to \infty} \cos\left(\frac{8}{n}\right) = \cos\left(\lim_{n \to \infty} \frac{8}{n}\right) = \cos(0) \] 3. **Evaluate the Cosine Function at the Limit:** \[ \cos(0) = 1 \] 4. **Conclusion:** Therefore, the limit of the sequence \( a_n \) as \( n \) approaches infinity is: \[ \lim_{n \to \infty} a_n = 1 \] **Answer:** The sequence approaches 1. Its limit is 1.