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.