Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (assume that n begins with 1.) - 8, 16 3, - 32 9, 64 27, - 128 81, ...

Your sequence

-8, 16/3, - 32/9, 64/27

is a geometric sequence with first term - 8 and common ratio

(16/3) / (-8) = (-32/9) / (16/3) = - 2/3

The general term an of a geometric sequence with first term a1 and ratio r is given by

an = a1·r^ (n-1)

For your sequence, this is

an = - 8· (-2/3) ^ (n-1)