Consider $9$ terms $a_1,a_2 \cdots a_9$ in Harmonic Progression with $a_4=5,a_5=4$. Find the value of the determinant $$\begin{vmatrix}a_1&a_2&a_3\\a_4&5&4\\ a_7&a_8&a_9\end{vmatrix}$$ The 'not so good ' method is clear, calculating the terms and then evaluating, but I want to ask if there exists a beautiful or elegant solution. Something I am missing. Thanks.
2026-04-23 11:25:26.1776943526
Find the value of a determinant in which the entries are in Harmonic Progression
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