Question

1. (0 points) write the first five terms of the recursive sequence.

\\a_1 = 4 \quad \text{and} \quad a_{n+1} = 1 + \frac{1}{a_n}\\

Explanation:

Step1: Identify the first term

$$a_1 = 4$$

Step2: Calculate the second term

$$a_2 = 1 + \frac{1}{a_1} = 1 + \frac{1}{4} = \frac{5}{4}$$

Step3: Calculate the third term

$$a_3 = 1 + \frac{1}{a_2} = 1 + \frac{4}{5} = \frac{9}{5}$$

Step4: Calculate the fourth term

$$a_4 = 1 + \frac{1}{a_3} = 1 + \frac{5}{9} = \frac{14}{9}$$

Step5: Calculate the fifth term

$$a_5 = 1 + \frac{1}{a_4} = 1 + \frac{9}{14} = \frac{23}{14}$$

Answer:

\(a_1 = 4\), \(a_2 = \frac{5}{4}\), \(a_3 = \frac{9}{5}\), \(a_4 = \frac{14}{9}\), \(a_5 = \frac{23}{14}\)