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enter image description here In this problem I am not able to see how the convergence of the sequence depends on the first term .can anyone show me?

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    Well, if you use the given recurrence equation you'll see that the sequence increases and decreases when you start from $0.5$ and $1.5$ respectively. Since each is bounded by the other, I think both converge to $1$. – 2017-02-18

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Hint: When $x_1=0.5$, the sequence is nondecreasing and $x_n \leq 1, ~\forall n$, that is the sequence is bounded above by $1$. Similarly starting with $1.5$ the sequence is nonincreasing and bounded below by $1$.