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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
Question 3
A periodic sequence is defined by $U_n = ext{sin}\left(\frac{n \pi}{2}\right)$ State the period of this sequence. Circle your answer. 8 2π 4 π
Worked Solution & Example Answer: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
Step 1
State the period of this sequence.
Answer
The period of the sine function is typically defined as . However, since the function includes a coefficient in front of , we need to adjust the period accordingly. Here, the argument of the sine function is , indicating that the input to sine completes one full cycle when:
Solving for gives:
Thus, the period of the sequence is 4.