(Solved): 1. The Fibonneci sequence is a sequence defined by the relation an=an1+an2 and initi ...

1. The Fibonneci sequence is a sequence defined by the relation $$a_n=a_{n?1}+a_{n?2}$$ and initial conditions $$a_1=1$$, $$a_2=1$$. (a) Find $$a_{10}$$. (b) Suppose we change the initial conditions to be $$a_1=3$$ and $$a_2=7$$. Find $$a_{10}$$ for this new sepuence, 2. Let $$b_n$$ be the sequenee defined by $$b_1=1$$, and $$b_n=3?b_{n?1}$$. (a) Find $$b_5$$ (b) Find a clased formula that generates this sequence. 3. Suppose $$c_n=5?c_{n?1}?6c_{n?2}$$ with $$c_1=6$$ and $$c_2=17$$ (a) Find $$c_3,c_4$$, and $$c_5$$. (b) Find the first 5 terms of the sequence defined by $$f(n)=2^{n?1}+5?3^{n?1}$$