Question
The Lucas numbers are defined recursively as follows:$$L_{1}=1, L_{2}=3, \text { and } L_{k}=L_{k-2}+L_{k-1} \text { for } k \geq 3$$What are $L_{3}, L_{4}, L_{5}$, and $L_{6} ?$
Step 1
According to the given recursive formula, $L_{3}=L_{3-2}+L_{3-1}=L_{1}+L_{2}=1+3=4$. Show more…
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