1.04f Sequence types: increasing, decreasing, periodic

The terms, \(u_n\), of a periodic sequence are defined by $$u_1 = 3 \quad \text{and} \quad u_{n+1} = \frac{-6}{u_n}$$

1. Find \(u_2\), \(u_3\) and \(u_4\) [2 marks]
2. State the period of the sequence. [1 mark]
3. Find the value of \(\sum_{n=1}^{101} u_n\) [2 marks]

Given \(u_1 = 1\), determine which one of the formulae below defines an increasing sequence for \(n \geq 1\) Circle your answer. [1 mark] \(u_{n+1} = 1 + \frac{1}{u_n}\) \quad \(u_n = 2 - 0.9^{n-1}\) \quad \(u_{n+1} = -1 + 0.5u_n\) \quad \(u_n = 0.9^{n-1}\)

A sequence is defined by $$u_1 = 3$$ $$u_{n+1} = 2 - \frac{4}{u_n}, \quad n \geq 1$$ Find the exact values of

1. \(u_2\), \(u_3\) and \(u_4\) [3]
2. \(u_{61}\) [1]
3. \(\sum_{i=1}^{99} u_i\) [3]