1. The problem asks: Given the recurrence relation for the number of ways to climb stairs where $S_1=1$, $S_2=2$, and $S_n=S_{n-1}+S_{n-2}$, find the number of ways to climb 8 stairs. 2. This is a classic Fibonacci-type sequence where each term is the sum of the two previous terms. 3. Let's calculate step-by-step: - $S_1=1$ - $S_2=2$ - $S_3=S_2+S_1=2+1=3$ - $S_4=S_3+S_2=3+2=5$ - $S_5=S_4+S_3=5+3=8$ - $S_6=S_5+S_4=8+5=13$ - $S_7=S_6+S_5=13+8=21$ - $S_8=S_7+S_6=21+13=34$ 4. Therefore, the number of ways to climb 8 stairs is $\boxed{34}$. This sequence counts all possible ways to climb stairs taking either 1 or 2 steps at a time.