In online platforms, recommender systems are responsible for directing users to relevant content. In order to enhance the users' engagement, recommender systems adapt their output to the reactions of the users, who are in turn affected by the recommended content. In this work, we study a tractable analytical model of a user that interacts with an online news aggregator, with the purpose of making explicit the feedback loop between the evolution of the user's opinion and the personalised recommendation of content. More specifically, we assume that the user is endowed with a scalar opinion about a certain issue and receives news about it from a news aggregator: her opinion is influenced by all received pieces of news, which are characterized by a binary position on the issue at hand. The user is affected by a confirmation bias, that is, a preference for news that confirm her current opinion. The news aggregator recommends items with the goal of maximizing the number of user's clicks (as a measure of her engagement): in order to fulfil its goal, the recommender has to compromise between exploring the user's preferences and exploiting what it has learned so far. After defining suitable metrics for the effectiveness of the recommender systems (such as the click-through rate) and for its impact on the opinion, we perform both extensive numerical simulations and a mathematical analysis of the model. We find that personalised recommendations markedly affect the evolution of opinions and favor the emergence of more extreme ones: the intensity of these effects is inherently related to the effectiveness of the recommender. We also show that by tuning the amount of randomness in the recommendation algorithm, one can seek a balance between the effectiveness of the recommendation system and its impact on the opinions.