Question

The Lucas sequence Ln is defined by the recurrence relation: Ln = Ln−1 + Ln−2, for n ≥ 3, with L1 = 1 and L2 = 3. Which one of the options given is TRUE?

• A. $L_n=(\frac{1+\sqrt5}{2})^n+(\frac{1-\sqrt5}{2})^n$
• B. $L_n=(\frac{1+\sqrt5}{2})^n-(\frac{1-\sqrt5}{3})^n$
• C. $L_n=(\frac{1+\sqrt5}{2})^n+(\frac{1-\sqrt5}{3})^n$
• D. $L_n=(\frac{1+\sqrt5}{2})^n-(\frac{1-\sqrt5}{2})^n$

Answer 1

Answer: (A)

$L_n=(\frac{1+\sqrt5}{2})^n+(\frac{1-\sqrt5}{2})^n$

Answer 2

The correct option is (A)