Arsenal may end the season in second place if they are able to keep their consistency because, as you said, Manchester City, Chelsea, and Nottingham Forest are also fighting for the second position in the Premier League competition, although it is not that Arsenal did not have the target you are saying, but I think they don’t have the mentality to keep their consistency from the start of the season till the end of the season, and that is their problem. Sometimes I think it’s from the coach, though. They always are a challenging team but are unable to win the trophy.
Since this is the Premier League and there are still 10 matches left if this week is finished, then this will still be a competition that will occur until the end of the season, there is a possibility for a change in the standings so that at the end of the season we will see a different position at least in the top 4 of the standings. Liverpool is the favorite to become champion, currently they are leading by a fairly large point difference too. This is an opportunity for them to win the Premier League title from Manchester City who have managed to defend it for 4 seasons in a row.
Well, Liverpool do have a lot of point with which they are ahead of Arsenal who is right there at their bank, while Arsenal also are ahead of Nottingham forest with a fair number of points as well.
Maintaining the second position is or can be very easy for Arsenal if they only will learn to be consistent in winning all the games they currently have to play before the season comes to an end, this is assuming Nottingham forest and Manchester city are both consistent enough to win all their remaining games as well, then we can say or assume that the current season will come to an end with all the clubs maintaining their current position.
So going by this, we can already be saying congratulations to Liverpool for succeeding in breaking Manchester city's four winning streaks for the EPL title, but then, this is still too early to say since even a minute can change alot in football.