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Home » r^3 = 288 \times \frac34 = 216 - 500apps

r^3 = 288 \times \frac34 = 216 - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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$$Question: A statistician models a time series using a geometric sequ...
The sum of the first five terms of a geometric sequence with first ter...
S_5 = 3(1 + r + r^2 + r^3 + r^4) = 3 \cdot rac{r^5 - 1}{r - 1} \quad...
e 1 ext{)}
We want:
\cdot rac{r^5 - 1}{r - 1} > 300
rac{r^5 - 1}{r - 1} > 100
We test integer values of $ r > 1 $ (since $ r = 1 $ gives $ S_5 = 15...
For $ r = 2 $:
rac{32 - 1}{2 - 1} = 31 \quad \Rightarrow \quad 3 \cdot 31 = 93 < 300

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