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Home » Then, \( n^2 + (n+1)^2 = 365 \). - Dachbleche24

Then, \( n^2 + (n+1)^2 = 365 \). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Alternatively: The volumes form a geometric sequence with first term \(a = 729\), ratio \(r = 1/2\), and we want the number of terms \(n\) such that the sum \(S_n \geq 729\). But sum starts at 729, so \(n=1\). Not useful.

📌 Correct model: The volumes are:

📌 \(V_1 = 729\)

📌 \(V_2 = 729 \times 1/2 = 364.5\)

📌 But 364.5 < 729, so only one bottle fits.

📌 But question implies multiple.

📌 Insight: Perhaps "each holds half of the previous" starts after the first, and the first is 729, second is 364.5, but the *total* to be poured is more? But it’s only 729.

📌 Another possibility: The initial 729 ml is split into portions where each portion is half the size of the container that holds it, and containers are nested with halving capacity. But we are to find how many containers are used to hold the entire volume if each subsequent container holds half the previous.

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