Question

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 , ...

Answer 1

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)