A problem of seconds in seconds

Algebra Level 3

\[ \large \sum_{z=1}^{2016} r_{z}=?\] where \(r_{z}\) is the \(z^{th}\) term of a sequence of distinct real numbers such that \( r_1=0 \), \( r_{2016}=2 \) and \( |r_{n+1}-r_n| \) is constant.

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