To start you off, let . Then . But the sequence is increasing, and , so it follows that . In other words, . Therefore the only possibility is that .
Thus and . Therefore , and . But if and then and have to fit in between 6 and 9 (because the sequence is increasing). The only way that can happen is if and .
Continue exploring in that way, using the facts that and that the sequence is increasing. You will find that is uniquely determined for each . After a while, a pattern should emerge, which will enable you to predict and