Moderate -0.5 This is a straightforward Further Maths question requiring basic sequence evaluation and pattern recognition. Part (a) involves computing sine values at standard angles (routine trigonometry), while part (b) is a simple recurrence relation requiring backward iteration. The 'describe behaviour' aspect requires only observing periodicity/oscillation in (a) and linear growth in (b), which are standard observations requiring no deep insight.
For each of the following sequences, find the first 5 terms, \(u _ { 1 }\) to \(u _ { 5 }\). Describe the behaviour of each sequence.
a) \(\quad u _ { n } = \sin \left( \frac { n \pi } { 2 } \right)\)
b) \(u _ { 6 } = 33 , u _ { n } = 2 u _ { n - 1 } - 1\)
For each of the following sequences, find the first 5 terms, $u _ { 1 }$ to $u _ { 5 }$. Describe the behaviour of each sequence.
a) $\quad u _ { n } = \sin \left( \frac { n \pi } { 2 } \right)$\\
b) $u _ { 6 } = 33 , u _ { n } = 2 u _ { n - 1 } - 1$
\hfill \mbox{\textit{WJEC Unit 3 2022 Q9}}