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Home » Subtracting equation (2) from (3): - Malaeb

Subtracting equation (2) from (3): - Malaeb

📅 May 4, 2026 👤 scraface

May 04, 2026

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Total time: \( \frac{d}{60} + \frac{d}{90} = 5 \).
Solve: \( \frac{3d + 2d}{180} = 5 \) gives \( 5d = 900 \), so \( d = 1...
The sum of the first \( n \) terms of an arithmetic sequence is given...
Substitute: \( 210 = \frac{n}{2}(2 \times 3 + (n-1) \times 2) = \frac{...
Simplify: \( 210 = n(n + 2) \) → \( n^2 + 2n - 210 = 0 \).
Solve quadratic: \( n = \frac{-2 \pm \sqrt{4 + 840}}{2} = \frac{-2 \pm...
Positive root: \( n = \frac{27.02}{2} \approx 13.51 \), so \( n = 14 \...
Verify: \( S_{14} = \frac{14}{2}(6 + 26) = 7 \times 32 = 224 \) → too...
Try \( n = 13 \): \( S_{13} = \frac{13}{2}(6 + 24) = 6.5 \times 30 = 1...
Recheck equation: \( n(n + 2) = 210 \) → \( n^2 + 2n - 210 = 0 \).

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