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Triangle with sides as consecutive terms of a sequence.

Source: ILL 1979-35

June 2, 2011
geometryinductionarea of a triangleHeron's formulainequalities proposedinequalities

Problem Statement

Given a sequence (an)(a_n), with a1=4a_1 = 4 and an+1=an2−2(∀n∈N)a_{n+1} = a_n^2-2 (\forall n \in\mathbb{N}), prove that there is a triangle with side lengths an−1,an,an+1,a_{n-1}, a_n, a_{n+1}, and that its area is equal to an integer.
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