F(n) = f(n – 1) + f(n – 2); f(1) = 2; f(2) = 1.

list the first six terms of the sequence.

Work Shown:

f(1) = 2 is the first term

f(2) = 1 is the second term

Plug in n = 3. We add the first two terms to get the third term

f(n) = f(n-1)+f(n-2)

f(3) = f(3-1)+f(3-2)

f(3) = f(2)+f(1)

f(3) = 1+2

f(3) = 3

Now plug in n = 4 to get the fourth term

f(n) = f(n-1)+f(n-2)

f(4) = f(4-1)+f(4-2)

f(4) = f(3)+f(2) <<-- adding 3rd and 2nd term to get the 4th term

f(4) = 3+1

f(4) = 4

Repeat for n = 5.

f(n) = f(n-1)+f(n-2)

f(5) = f(5-1)+f(5-2)

f(5) = f(4)+f(3) <<-- adding 4th and 3rd term to get the 5th term

f(5) = 4+3

f(5) = 7

and the same for n = 6

f(n) = f(n-1)+f(n-2)

f(6) = f(6-1)+f(6-2)

f(6) = f(5)+f(4) <<-- adding 5th and 4th term to get the 6th term

f(6) = 7+4

f(6) = 11