Given:
The sequence is
an+1=an1+an
. (1)
The first term of the sequence is
a1=2
.
Calculation:
Obtain the second term of the sequence.
Substitute 1 for n in equation (1).
a1+1=a11+a1
a2=a11+a1
(2)
Substitute 2 for
a1
in equation (2).
a2=21+2=23
Thus, the second term of the sequence is
a2=23_
.
Obtain the third term of the sequence.
Substitute 2 for n in equation (1).
a2+1=a21+a2
a3=a21+a2
(3)
Substitute
23
for
a2
in equation (3).
a3=231+23=233+23=25
Thus, the third term of the sequence is
a3=25_
.
Obtain the fourth term of the sequence.
Substitute 3 for n in equation (1).
a3+1=a31+a3
a4=a31+a3
(4)
Substitute
25
for
a3
in equation (4).
a4=251+25=235+23=27
Thus, the fourth term of the sequence is
a4=27_
.
Obtain the fifth term of the sequence.
Substitute 4 for n in equation (1).
a4+1=a41+a4
a5=a41+a4
(4)
Substitute
27
for
a4
in equation (4).
a5=271+27=237+23=29
Thus, the fifth term of the sequence is
a5=29_
.
Therefore, the first five terms of the sequence are
2,23,25,27,29
.