Let {an} be the sequence given by ao = 2, a = 1 and an+2 =...

    

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Let {an} be the sequence given by ao = 2, a = 1 and an+2 = an+1+an for all nZ, n 0. Let {b} be the sequence given by bo = 0, b = 1 and bn = bn-1 + bn-2 for all n Z, n 2. (a) Find a2, a3, a4, as and a6. (b) Find b, b3 and b4. (c) Prove that 5bn+2 =an+4 - an for all n Z, n 1. (d) Prove that an = bn-1+bn+1 for all n Z, n 2. Let {an} be the sequence given by ao = 2, a = 1 and an+2 = an+1+an for all nZ, n 0. Let {b} be the sequence given by bo = 0, b = 1 and bn = bn-1 + bn-2 for all n Z, n 2. (a) Find a2, a3, a4, as and a6. (b) Find b, b3 and b4. (c) Prove that 5bn+2 =an+4 - an for all n Z, n 1. (d) Prove that an = bn-1+bn+1 for all n Z, n 2.