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