What are the first five terms of the sequence defined by the given function?
(1) = -6
f(n) = }(n − 1) + 2, for n = 2, 3, 4,
o a. 6,-4,-2,0, 2
b. 2, 8, 14, 20, 26
c. 6,-8.-10.-12, -14
d. 2.-4.-10.-16, -22

-6,-4,-2,0,2

is the answer if I interpreted your recursive sequence equation correctly.

Step-by-step 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.