Suppose { $X_{n}$}$_{n=1}$$^{infty}$ sequence of finite dimensional Banach spaces and suppose that X is either a closed subspace of (equation omitted) or a closed subspace of (equation omitted) with p>2. We show that every bounded linear operator from X to a Banach space Y of cotype q(2$leq$q〈p) is compact.t.t.