Question

Write the first five terms of the sequence with the given nth term. an = cos n 2

Answer 1

The first five terms of the sequence with the given n-th term $a_n = cos(\frac{n\pi}{2} )$ are : 0, -1, 0, 1, 0

For given question,

We have been given the n-th term of the sequence $a_n = cos(\frac{n\pi}{2} )$

We need to find the first five terms of the sequence.

For n = 1

$\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0$

For n = 2,

$\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1$

For n = 3,

$\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0$

For n = 4,

$\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1$

For n = 5,

$\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0$

Therefore, the first five terms of the sequence with the given n-th term$a_n = cos(\frac{n\pi}{2} )$ are : 0, -1, 0, 1, 0

Learn more about the sequence here:

https://brainly.com/question/4626313

#SPJ4