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The first five terms of the sequence with the given n-th term [tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
For given question,
We have been given the n-th term of the sequence [tex]a_n = cos(\frac{n\pi}{2} )[/tex]
We need to find the first five terms of the sequence.
For n = 1
[tex]\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0[/tex]
For n = 2,
[tex]\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1[/tex]
For n = 3,
[tex]\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0[/tex]
For n = 4,
[tex]\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1[/tex]
For n = 5,
[tex]\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0[/tex]
Therefore, the first five terms of the sequence with the given n-th term[tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
Learn more about the sequence here:
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