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Home » \(25a = -4\), \(a = -\frac425\) - Veritas Home Health

\(25a = -4\), \(a = -\frac425\) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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a \cdot ar \cdot ar^2 \cdot ar^3 = a^4 r^{6} = 160000
From the product:
a^4 r^6 = 160000 = 16 \cdot 10000 = 16 \cdot 10^4 = (2^4)(10^4) = (2 \...
a^4 r^6 = 20^4 \Rightarrow (ar^{1.5})^4 = 20^4 \Rightarrow ar^{1.5} =...
Letâs write $ a = rac{20}{r^{1.5}} $. Substitute into the sum:
rac{20}{r^{1.5}} (1 + r + r^2 + r^3) = 120
\Rightarrow rac{20(1 + r + r^2 + r^3)}{r^{1.5}} = 120
\Rightarrow rac{1 + r + r^2 + r^3}{r^{1.5}} = 6
Try $ r = 1 $:
rac{1 + 1 + 1 + 1}{1} = 4 < 6

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