  Hyers-Ulam stability of the sequence $ \{z_n\}_{n \in \mathbb{N}} $ generated
by linear maps is studied. The difference equation $ z_{n+1} = g_n(z_n) $ where
$ g_n(z) = a_nz + b_n $ and $ a_n \neq 0 $. Hyers-Ulam stability is determined
by the the limit of the geometric average of $ a_n $ rather than the type of
each linear maps. In particular, if $ \prod_{j=1}^{n-1}|a_j| $ is
subexponentially increasing sequence, then $ \{z_n\}_{n \in \mathbb{N}} $ has
no Hyers-Ulam stability. Other complementary results are also established with
properties of $ \prod_{j=1}^{n-1}|a_j| $. This result contains Hyers-Ulam
stability of the first order difference equation with periodic coefficients
also.
