- B If Q Satisfies Q2 Q 1 And We Define An Qn Then We Can Show That An An 1 An 2 In This Case We Say That Sequence 1 (226.62 KiB) Viewed 66 times
b) If q satisfies q2=q+1 and we define an=qn, then we can show that an=an−1+an−2. In this case, we say that sequence
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b) If q satisfies q2=q+1 and we define an=qn, then we can show that an=an−1+an−2. In this case, we say that sequence
b) If q satisfies q2=q+1 and we define an=qn, then we can show that an=an−1+an−2. In this case, we say that sequence an has the same recursive relation as the Fibonacci Sequence. Find all possible values of q that satisfies q2=q+1. (NOTICE that you should find two such q values, denoted by q1 and q2⋅) c) Let c1 and c2 be two numbers. If we define bn=c1q1n+c2q2n, then it can be shown that bn=bn−1+bn−2. Find the proper values of c1 and c2 such that b0=f0 and b1=f1, then compute the first 11 terms b0,b1,…,b10. d) compare the first 11 terms of fn and bn, what can you conclude? Does fn=bn for all n and why?