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 Pure - Question 3 - 2018 - Paper 1

The period of the sine function is typically defined as $2\pi$. However, since the function includes a coefficient in front of $n$, we need to adjust the period accordingly. Here, the argument of the sine function is $\frac{n \pi}{2}$, indicating that the input to sine completes one full cycle when:

$\frac{n \pi}{2} = 2\pi$

Solving for $n$ gives:

$n = \frac{2\pi \cdot 2}{\pi} = 4$

Thus, the period of the sequence $U_n$ is 4.