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Home » #### 10th term: 41 - jntua results

#### 10th term: 41 - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 a^4 r^6 = 20^4 \Rightarrow (ar^{1.5})^4 = 20^4 \Rightarrow ar^{1.5} = 20

📌 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

📌 Try $ r = 2 $:

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Solve the quadratic equation \( 2x^2 - 4x - 6 = 0 \) using the quadrat...
The quadratic equation is \( 2x^2 - 4x - 6 = 0 \), where \( a = 2 \),...
Calculate the discriminant:
\[ b^2 - 4ac = (-4)^2 - 4(2)(-6) \]
\[ b^2 - 4ac = 16 + 48 \]
\[ b^2 - 4ac = 64 \]
\[ x = rac{-(-4) \pm \sqrt{64}}{2(2)} \]
\[ x = rac{4 \pm 8}{4} \]
Calculate the two solutions:
\( x = rac{4 + 8}{4} = rac{12}{4} = 3 \)

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