Find an equation for the nth term of the arithmetic sequence.

a14 = -33, a15 = 9

For an arithmetic sequence the nth term can be solved by the equation, 
                           an = a1 + (n - 1) x d
where d is the common difference and an and a1 is the nth and first term, respectively. Shown below is the calculation for d and a1. 
                          d = (a15 - a14) / (15 - 14) = (9 - -33) / 1 = 42

               a14 = a1 + (n - 1) x d   ;   -33 = a1 + (14 - 1) x 42   ;   a1 = -579

Therefore, the general equation for the nth term of the given arithmetic sequence is    
                                   an = -579 + (n - 1) x 42