Suppose that integers c, d such that and are positive integers such that b2 – 2a? = 1. Prove that there exist positive are consecutive terms in some Farey sequence and а, a V2 d' (Hint: guess expressions for C, d in terms of a, b that seem to work, then prove that they do.)

Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: Which of the following a = a-1 + 2a-2 +2n-9 a. ¹2+2-5(-1)" b. -n-2+5(-1)* C.n+2+5(-1)" -n+2+5(-1)"…

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Q: (a) Find the product a b, given that a = b = √9-√√9-√9-√7. b) Find all sequences a1, a2, a3,....of…

A: as per company guidelines we solve only first question when multiple question being posted