Answer:
[tex]A(1)=9[/tex]
[tex]A(2)=4[/tex]
[tex]A(3)=-1[/tex]
Arithmetic sequence
Step-by-step explanation:
We are given that
[tex]A(n+1)=A(n)-5 \;for\;n\geq 1[/tex] A(1)=9
We have to find first three terms and identify the sequence is geometric or arithmetic.
Substitute n=1
Then, we get
[tex]A(2)=A(1)-5=9-5=4[/tex]
For n=2
[tex]A(3)=A(2)-5=4-5=-1[/tex]
For n=3
[tex]A(4)=-1-5=-6[/tex]
[tex]d_1=A_2-A_1=4-9=-5[/tex]
[tex]d_2=A_3-A_2=-1-4=-5[/tex]
[tex]d_3=A_4-A_3=-6+1=-5[/tex]
[tex]d_1=d_2=d_3=-5[/tex]
When the difference of consecutive terms are constant then the sequence is arithmetic sequence.
Therefore, given sequence is arithmetic sequence.
