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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: Mechanics - Question 3 - 2018 - Paper 1

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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. Circle your answer. 8 2$ \pi$ 4 $ \pi$

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: Mechanics - Question 3 - 2018 - Paper 1

Step 1

State the period of this sequence.

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Answer

The function Un=extsin(nπ2)U_n = ext{sin} \left( \frac{n\pi}{2} \right) is a periodic function. The period of the sine function is 2pi2\\pi. To find the period for this specific sequence, we analyze the argument:

Let's set: nπ2+2π=(n+P)π2n\frac{\pi}{2} + 2\pi = (n + P)\frac{\pi}{2}

Where PP is the period.

By simplifying, we derive: P=4P = 4

Thus, the period of the sequence is 4.

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