Q5

MCQ1 mark, −0.33

The Lucas sequence $L_{n}$ is defined by the recurrence relation:

L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3,

with $L_{1}=1$ and $L_{2}=3$ . Which one of the options given is TRUE?

(A)

$L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}+\left(\frac{1-\sqrt{5}}{2}\right)^{n}$

(B)

$L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{3}\right)^{n}$

(C)

$L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}+\left(\frac{1-\sqrt{5}}{3}\right)^{n}$

(D)

$L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$

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