A series of natural numbers $F_1, F_2, F_3, F_4, F_5, F_6, F_7, \dots$ obeys $F_{n+1} = F_n + F_{n-1}$ for all integers $n \ge 2$ . If $F_6 = 37$, and $F_7 = 60$, then what is $F_1$ ?

The given recurrence relation is:

Rearranging this to express each term in terms of the subsequent two terms:

Given $F_7 = 60$ and $F_6 = 37$, we can compute backwards:

1. $F_5 = F_7 - F_6 = 60 - 37 = 23$

2. $F_4 = F_6 - F_5 = 37 - 23 = 14$

3. $F_3 = F_5 - F_4 = 23 - 14 = 9$

4. $F_2 = F_4 - F_3 = 14 - 9 = 5$

5. $F_1 = F_3 - F_2 = 9 - 5 = 4$

Thus, $F_1 = 4$, which corresponds to Option (A).