A periodic sequence is defined by $U_n = ext{sin} \left( \frac{n\pi}{2} \right)$ State the period of this sequence - AQA - A-Level Maths Mechanics - Question 3 - 2018 - Paper 1

The function $U_n = ext{sin} \left( \frac{n\pi}{2} \right)$ is a periodic function. The period of the sine function is $2\\pi$. To find the period for this specific sequence, we analyze the argument:

Let's set: $n\frac{\pi}{2} + 2\pi = (n + P)\frac{\pi}{2}$

Where $P$ is the period.

By simplifying, we derive: $P = 4$

Thus, the period of the sequence is 4.