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Investigate special cases for small $n$ first.
Can you spot patterns in the sums for $n=3$, $4$, $5$, $6$, $7 \dots$?
In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?