We identify minimal and dominant solutions of three-term recurrence relations for the confluent hypergeometric functions $_1F_1(a+\epsilon_1 n;c+\epsilon_2 n;z)$ and $U(a+\epsilon_1 n,c+\epsilon_2 n,z)$, where $\epsilon_i=0,\pm 1$ (not both equal to 0). The results are obtained by applying Perron's theorem, together with uniform asymptotic estimates derived by T.M. Dunster for Whittaker functions with large parameter values. The approximations are valid for complex values of $a$, $c$ and $z$, with $|{\rm arg}\,z|<\pi$.