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
