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Home » The Ultimate Guide to Redeeming VBucks Before They Expire – Act Now! - jntua results

The Ultimate Guide to Redeeming VBucks Before They Expire – Act Now! - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A geometric sequence has first term 4 and common ratio \( \frac{3}{2} \). What is the sum of the first 5 terms?

📌 Sum of geometric sequence: \( S_n = a \frac{r^n - 1}{r - 1} \),

📌 \( a = 4 \), \( r = \frac{3}{2} \), \( n = 5 \).

📌 \( S_5 = 4 \cdot \frac{(\frac{3}{2})^5 - 1}{\frac{3}{2} - 1} = 4 \cdot \frac{\frac{243}{32} - 1}{\frac{1}{2}} = 4 \cdot \frac{\frac{211}{32}}{\frac{1}{2}} = 4 \cdot \frac{211}{32} \cdot 2 = 8 \cdot \frac{211}{32} = \frac{1688}{32} = 52.75 \).

📌 As fraction: \( \frac{1688}{32} = \frac{211}{4} \).

📌 #### \( \frac{211}{4} \)

📌 Combine logs: \( \log_2(x(x - 2)) = 3 \) → \( x(x - 2) = 2^3 = 8 \).

📌 So, \( x^2 - 2x - 8 = 0 \) → factor: \( (x - 4)(x + 2) = 0 \).

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