(sum (range 1 365))

assuming you defined these already; I have them in my utils library ;-)

  (defun range (start end)
    (loop for x from start to end collecting x))

  (defun sum (sequence)
    (reduce #'+ sequence))

didn't even think of that one! :)

or plain math: n(n+1)/2

How quickly can you generalize the plain math formula to these sequences: http://www.research.att.com/njas/sequences/index.html