# Fibonacci sequence

#### TABASSUM

Hi can anyone explain how i can get express Fn+3 in terms of Fn+2 and Fn to show that Fn+2 = 1/2(Fn+3 + Fn). Any help is much appreciated

#### MarkFL

I would begin with:

(1) $$\displaystyle F_{n+2}=F_{n+1}+F_{n}$$

(2) $$\displaystyle F_{n+3}=F_{n+2}+F_{n+1}$$

Now, solve (2) for $$\displaystyle F_{n+1}$$ and substitute into (1), then solve for $$\displaystyle F_{n+2}$$.

1 person

#### TABASSUM

Thankyou so much.