This is my first time,I was wondering if I leave my cider for say 3 weeks instead of the recommended 7-10 days,will this improve it?
Normally, cider is conditioned longer than three weeks. Cider can be very sour because of the malic acid contained in it. However, this can (or will) be converted through malolactic fermentation, which transforms the malic acid into lactic acid. This is the reason that traditional French cider is conditioned for a couple of months. Apparently this fermentation can also lead to off-flavors, and letting it condition longer removes them.
It depends on your cider and the yeast, oand/or any other buigs you have in there.
Once you malolactate fermentations and cleanup has occured there can still be a number of chemical processes going on that will continue to change the flavour of your cider over time.
Your main question will this improve it, is subjective byt the generally accepted answer is yes it will. But, it depends on what you like and your cider.