Question

Question/picture attached below:
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Answer 1

Since each side of the xylophone has "n" wooden bars and there is an extra one in the centre, do we treat this as two series?

Answer 2

well, there are \(2n+1\) bars, so the \(2n\) are from the left,right side, and then the \(1\) is the middle. so you can just model it as the middle plus double a series for both sides

Answer 3

hmm.. so what if i did something like this?
\[S = \frac{ n }{ 2 } (20 + n(n-1)b) + \frac{ n+1 }{ 2 }(20 + nb) \]

Answer 4

Just tested it by expanding and i eventually proved S = bn^2 + 20n + 10 so i guess it works :)