Consider the sequence: \[65, 42, 67, 44, 69, 46, 71, 48 \, \ldots\]

The \(n^\text{th}\) term of this sequence can be expressed as \(an+b(-1)^n +c\), where \(a,b,c \in \mathbb{Z}\).

Evaluate \(a+b+c\).

Note: The 1st term of the sequence can be expressed as \( a \times 1 + b(-1)^2 + c \).

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