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
.