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does gargling salt water cure a sore throat - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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T(1) = 4, \quad T(n) = 2T(n-1) + 3 \text{ for } n \geq 2.
We compute $ T(n) $ for $ n = 1 $ to $ 5 $:
$ T(1) = 4 $
$ T(2) = 2 \cdot 4 + 3 = 8 + 3 = 11 $
$ T(3) = 2 \cdot 11 + 3 = 22 + 3 = 25 $
$ T(4) = 2 \cdot 25 + 3 = 50 + 3 = 53 $
$ T(5) = 2 \cdot 53 + 3 = 106 + 3 = 109 $
Now compute the sum:
S(5) = T(1) + T(2) + T(3) + T(4) + T(5) = 4 + 11 + 25 + 53 + 109 = 202
Thus, the total energy over the first 5 segments is $ \boxed{202} $.

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