22/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3. which formula can be used to describe the sequence?

Your sequence appears to be geometric with a common ratio of 2. It can be described by
  a(n) = (-2 2/3)·2^(n-1)


This can be written in a number of other forms, including
  a(n) = (-8/3)·2^(n-1)
  a(n) = (-1/3)·2^(n+2)
  a(n) = (-4/3)·2^n