If everything is already written, why should we do good deeds?

The Companions of the Prophet ﷺ put this question to him, and his answer was that they should perform good deeds.

Among the articles of faith is belief in Qadr, predestination: that all decrees, general and particular, have been recorded in advance.

Ali may Allah be pleased with him reported that one day Allah's Messenger ﷺ was sitting with a wood in his hand and he was scratching the ground. He raised his head and said, "There is not one amongst you who has not been allotted his seat in Paradise or Hell." The Companions said, "Allah's Messenger ﷺ! then, why should we perform good deeds, why not depend upon our destiny?" Thereupon, he said, "No, do perform good deeds, for everyone is facilitated in that for which he has been created"; then he recited this verse: "Then, who gives to the needy and guards against evil and accepts the excellent (the truth of Islam and the path of righteousness it prescribes), We shall make easy for him the easy end..." [Qur'an, al-Layl 92:5-10] [Sahih Muslim 2647]