Here's the terrifying thing; it probably wouldn't take a hundred years or our trust for this to happen. This is making some strong assumptions, but the first AI could probably improve itself. Making better AIs that make better AIs and so on. Very rapidly (possibly only hours, days, weeks) it could become much much smarter than humans. If that happens, than we don't know what's possible, but it could probably do a lot of things we consider impossible. Like hack computer networks trivially and spread itself through the entire internet. Solve the protein folding problem and design working nanotech.

Within a week it could pay/blackmail/manipulate some humans somewhere into developing some crude self-replicating robots or nanotech. Then almost immediately afterwards it consumes the entire Earth in a swarm of rapidly self-replicating nanobots.

...or something. How should I know what a mind literally millions of times more intelligent than me would do. It's like predicting the exact next move a chessmaster will make. I don't know, but I'm confident they'd beat me quickly.

The goal, of course, is to make an AI which won't do this. If the AI decides to terminate the human race, we've already failed making it friendly and it obviously doesn't share our goals and values. But what are our goals and values? I don't know if anyone can answer that. I'm not sure if there is a satisfactory answer.