Determine all sequences of real numbers $a_1$, $a_2$, $\ldots$, $a_{1995}$ which satisfy: \[ 2\sqrt{a_n - (n - 1)} \geq a_{n+1} - (n - 1), \ \mbox{for} \ n = 1, 2, \ldots 1994, \] and \[ 2\sqrt{a_{1995} - 1994} \geq a_1 + 1. \]
Source: APMO 1995
Tags: algebra unsolved, algebra
Determine all sequences of real numbers $a_1$, $a_2$, $\ldots$, $a_{1995}$ which satisfy: \[ 2\sqrt{a_n - (n - 1)} \geq a_{n+1} - (n - 1), \ \mbox{for} \ n = 1, 2, \ldots 1994, \] and \[ 2\sqrt{a_{1995} - 1994} \geq a_1 + 1. \]