<Dl> <Dd> F n = φ n − (1 − φ) n 5, (\ displaystyle F_ (n) = (\ frac (\ varphi ^ (n) - (1 - \ varphi) ^ (n)) (\ sqrt (5))) \,,) </Dd> </Dl> <Dd> F n = φ n − (1 − φ) n 5, (\ displaystyle F_ (n) = (\ frac (\ varphi ^ (n) - (1 - \ varphi) ^ (n)) (\ sqrt (5))) \,,) </Dd> <P> a formula for φ n (\ displaystyle \ varphi ^ (n)) is obtained: </P> <Dl> <Dd> φ n = L n + F n 5 2 . (\ displaystyle \ varphi ^ (n) = ((L_ (n) + F_ (n) (\ sqrt (5))) \ over 2) \, .) </Dd> </Dl>

What is the 20th term of the lucas sequence