What is the sequence of the diagonals of a polygon?

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Answer 1 · 2017-04-20T20:01:15

${ (a_1 = 0), (a_2 = 0), (a_n = (n(n-3))/2" for "n >= 3) :}$

I think you are wanting to know what the number of diagonals of a convex $n$ sided polygon for any $n$ , with the resulting sequence.

A diagonal runs from one vertex to a distinct non-adjacent vertex, of which there are $n-3$ possibilities.

Hence the formula for the number of diagonals of an $n$ -sided convex polynomial is:

$(n(n-3))/2$

which is valid for any $n >= 3$

So we can define a corresponding sequence by:

${ (a_1 = 0), (a_2 = 0), (a_n = (n(n-3))/2" for "n >= 3) :}$

The first few terms are:

$0, 0, 0, 2, 5, 9, 14, 20,...$