Answer:
-6,-4,-2,0,2
is the answer if I interpreted your recursive sequence equation correctly.
Explanation:
I'm going to assume the following:
f(1)=-6
f(n)=f(n-1)+2
They alread give you the first term is -6.
So we want to find the next 4 terms.
The second term is given by f(2).
So we replace n with 2:
f(n)=f(n-1)+2 with n=2
f(2)=f(2-1)+2
f(2)=f(1)+2
f(2)=-6+2
f(2)=-4
The third term is given by f(3).
So we replace n with 3:
f(n)=f(n-1)+2 with n=3
f(3)=f(3-1)+2
f(3)=f(2)+2
f(3)=-4+2
f(3)=-2
The fourth term is given by f(4).
We are going to replace n with 4.
f(n)=f(n-1)+2 with n=4
f(4)=f(4-1)+2
f(4)=f(3)+2
f(4)=-2+2
f(4)=0
The fifth term is given by f(5).
We will replace n with 5.
f(n)=f(n-1)+2 with n=5
f(5)=f(5-1)+2
f(5)=f(4)+2
f(5)=0+2
f(5)=2
So the first 5 terms are given by the values of:
f(1),f(2),f(3),f(4),f(5).
The values we got in order are:
-6,-4,-2,0,2
This should also make sense from reading:
f(1)=-6
f(n)=f(n-1)+2
That bottom equation says to find a term you just add 2 to the previous term. They gave us the first term was -6 and told us just to add 2 to generate the terms after.
First term is -6.
Second term is -6+2=-4.
Third term is -4+2=-2.
Fourth term is -2+2=0
Fifth tern is 0+2=2.
In the future this sequence is called an arithmetic sequence because the term and previous term has the same difference; this is called a commom difference.