Question

1. (10 points) write the first five terms of the recursive sequence.

\\a_1 = 7 \quad \text{and} \quad a_{n+1} = 1 + \frac{1}{a_n}\\

Explanation:

Step1: Identify the first term

$$a_1 = 7$$

Step2: Calculate the second term

$$a_2 = 1 + \frac{1}{a_1} = 1 + \frac{1}{7} = \frac{8}{7}$$

Step3: Calculate the third term

$$a_3 = 1 + \frac{1}{a_2} = 1 + \frac{7}{8} = \frac{15}{8}$$

Step4: Calculate the fourth term

$$a_4 = 1 + \frac{1}{a_3} = 1 + \frac{8}{15} = \frac{23}{15}$$

Step5: Calculate the fifth term

$$a_5 = 1 + \frac{1}{a_4} = 1 + \frac{15}{23} = \frac{38}{23}$$

Answer:

\(7, \frac{8}{7}, \frac{15}{8}, \frac{23}{15}, \frac{38}{23}\)