Question

The Lucas numbers are defined by the recursive formula t1 = 2, t2 = 1, tn = tn - 1 + tn - 2, where n âN and n > 2. What are the first 9 Lucas numbers?

Answer 1

The first two are given to you, $t_1=2$ and $t_2=1$. Use the recursive formula to get the 3rd term; then use the 2nd and 3rd terms to get the 4th; and so on.

Since the n-th Lucas number is the sum of the previous two Lucas numbers, you have

$t_3 = t_2 + t_1 = 1 + 2 = 3$

$t_4 = t_3 + t_2 = 1 + 3 = 4$

$t_5 = t_4 + t_3 = 4 + 3 = 7$

$t_6 = t_5 + t_4 = 7 + 4 = 11$

$t_7 = t_6 + t_5 = 11 + 7 = 18$

$t_8 = t_7 + t_6 = 18 + 11 = 29$

$t_9 = t_8 + t_7 = 29 + 18 = 47$