Sequence

Algebra Level 3

Given that \(x_1, x_2, \ldots,x_{16} \) are positive real numbers such that \( \dfrac{x_1}{x_2} = \dfrac{x_2}{x_3} = \cdots = \dfrac{x_{15}} {x_{16}} \).

If \(x_1 + x_2 + x_3 + x_4 = 20 \) and \( x_5 + x_6 + x_7 +x_8 = 320 \), find \(x_{13} + x_{14} + x_{15} + x_{16} \).

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