# Sum of a series

**Number Theory**Level 4

A sequence \(\{T(n)\}_{n\geq 1}\) having first term \(T(1) = 1\) has subsequent terms defined by the following recurrence relation,

\[\frac{T(n + 1)}{T(n)} = \frac{7+(-1)^{n - 1}}{4}~\forall~n\geq 1\]

What is the units' digit of the sum of the first 2014 terms of the above defined sequence ?