To find: The first five terms of the sequence.

The first five terms of the sequence are 0,−1,0,1,0 .

Given:

The sequence is an=cosnπ2 . (1)

Calculation:

Obtain the first term of the sequence.

Substitute 1 for n in equation (1).

a1=cos1⋅π2   =cosπ2   =0

Thus, the first term of the sequence is a1=0_ .

Obtain the second term of the sequence.

Substitute 2 for n in equation (1).

a2=cos2⋅π2   =cosπ   =−1

Thus, the second term of the sequence is a2=−1_ .

Obtain the third term of the sequence.

Substitute 3 for n in equation (1).

a3=cos3⋅π2   =cos3π2   =0

Thus, the third term of the sequence is a3=0_ .

Obtain the fourth term of the sequence.

Substitute 4 for n in equation (1).

a4=cos4⋅π2   =cos2π   =1

Thus, the fourth term of the sequence is a4=1_ .

Obtain the fifth term of the sequence.

Substitute 5 for n in equation (1).

a5=cos5⋅π2   =cos5π2   =0

Thus, the fifth term of the sequence is a5=0_ .

Therefore, the first five terms of the sequence are 0,−1,0,1,0 .