Let a_1 and a_2 be arbitrary real number that are not equal. For [tex]n \geq 3[/tex], define a_n inductively by,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a_n = \frac{1}{2} (a_{n-1}+a_{n+2} )[/tex]

I cannot get the result that the book gets. I proceed,

[tex]a_{n+1} - a_{n} = \frac{1}{2}(a_n + a_{n-1} ) - \frac{1}{2} (a_{n-1} + a_{n-2} ) = \frac{1}{2} ( a_n - a_{n-2}

)= \frac{1}{2}(a_n + a_{n-1} ) [/tex]

The book got the answer,

[tex] a_{n+1} - a_n = \frac{-1}{2} (a_n - a_{n-1} ) [/tex]

Any help for me?

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# Cauchy sequence question

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