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## Main Question or Discussion Point

I understand that when a sequence is described recursively, for example: ##a_1=2, a_{n+1} = \sqrt{3a_n}## then we mean that the first term is 2, the second term is ##\sqrt{3*2} = \sqrt{6}##, the third term is ##\sqrt{3*\sqrt{6}}##, and so on.

What I do not understand is how to interpret the following recursively described sequence: ##a_0>0, a_{n+1} = \frac{6}{2a_n+1}##. What is the first term of this sequence? Does ##a_0>0## mean that the first term can be any natural number? Or that it can be any real number?

What I do not understand is how to interpret the following recursively described sequence: ##a_0>0, a_{n+1} = \frac{6}{2a_n+1}##. What is the first term of this sequence? Does ##a_0>0## mean that the first term can be any natural number? Or that it can be any real number?