i think it should be noted, though, that just because your arms feel fatigued does not mean you have a bad riding position, especially if you are new to riding. you should be able to hold yourself up with your core, but that doesn't mean you do when your arms are on the bars, they are always taking some of the weight.

when i started riding i was moving over from running, where my core was fine but my arms were little twigs. my triceps killed after every ride (over 10 miles or so). they didn't really hurt because i was putting all my weight on them, it was just my arms absorbing all the bumps and twists and turns of the front wheel. once i'd been riding a couple months my arms were up to par and i had no troubles.