# Zig-zag sequence

Algebra Level 4

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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