Question

Write the first five terms of the sequence. \(a_{n}=\sin \frac{n \pi}{2}\)

Short answer

The first five terms of the sequence are \(1, 0, -1, 0, 1\).

Step-by-step solution

Term 1

Substitute \(n=1\) into the function which gives \(a_{1}=\sin \frac{1 \pi}{2}\), and evaluating this expression gives \(a_{1}=1\)

Term 2

Substitute \(n=2\) into the function to get \(a_{2}=\sin \frac{2 \pi}{2}\), this simplifies to \(a_{2}=\sin (\pi)\), evaluating this yields \(a_{2}=0\)

Term 3

Substitute \(n=3\) into the function to get \(a_{3}=\sin \frac{3 \pi}{2}\), evaluating this yields \(a_{3}=-1\)

Term 4

Substitute \(n=4\) into the function to get \(a_{4}=\sin \frac{4 \pi}{2}\), this simplifies to \(a_{4}=\sin (2\pi)\), evaluating this gives \(a_{4}=0\)

Term 5

Substitute \(n=5\) into the function to obtain \(a_{5}=\sin \frac{5 \pi}{2}\), and upon evaluating this results in \(a_{5}=1\)