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Home » Let $ b_n $ = number of valid strings of length $ n $ ending in 3 - Network4

Let $ b_n $ = number of valid strings of length $ n $ ending in 3 - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 \(a = 50\), \(r = 1.2\), \(n = 5\)

📌 a_5 = 50 \cdot (1.2)^4 = 50 \cdot 2.0736 = 103.68 \approx 104

📌 Answer:** \(\boxed{104}\)

📌 Geometry – Solar Panel Surface Area

📌 A rectangular solar panel has length \(2x + 3\) meters and width \(x - 1\) meters. If the area is 40 m², find \(x\).

📌 2x^2 - 2x + 3x - 3 = 40 \Rightarrow 2x^2 + x - 43 = 0

📌 x = \frac{-1 \pm \sqrt{1^2 + 4 \cdot 2 \cdot 43}}{2 \cdot 2} = \frac{-1 \pm \sqrt{345}}{4}

📌 \(\sqrt{345} \approx 18.57\), so

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with $ a_1 = 2 $ (E, J), $ a_2 = 3 $ (EE, EJ, JE) — JJ is invalid.
$ a_1 = 2 $
$ a_2 = 3 $
$ a_3 = a_2 + a_1 = 3 + 2 = 5 $
$ a_4 = a_3 + a_2 = 5 + 3 = 8 $
$ a_5 = a_4 + a_3 = 8 + 5 = 13 $
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