A periodic sequence is defined by $U_n = (-1)^n$ State the period of the sequence - AQA - A-Level Maths Pure - Question 2 - 2022 - Paper 1

To find the period of the sequence defined by $U_n = (-1)^n$, we first evaluate the sequence for successive integer values of $n$:

• For $n = 0$: $U_0 = (-1)^0 = 1$
• For $n = 1$: $U_1 = (-1)^1 = -1$
• For $n = 2$: $U_2 = (-1)^2 = 1$
• For $n = 3$: $U_3 = (-1)^3 = -1$

From this evaluation, we notice that the sequence alternates between 1 and -1, which indicates a periodic behavior. The sequence results repeat every 2 terms, thus the period is 2.