QuestionJuly 23, 2025

Find the sum of the geometric series. -3-12-48-192,ldots n=6 -3320 -4095 1 -3692

Find the sum of the geometric series. -3-12-48-192,ldots n=6 -3320 -4095 1 -3692
Find the sum of the geometric series.
-3-12-48-192,ldots n=6
-3320
-4095
1
-3692

Solution
4.5(274 votes)

Answer

-4095 Explanation 1. Identify the first term and common ratio First term a = -3. Common ratio r = \frac{-12}{-3} = 4. 2. Use the formula for the sum of a geometric series **Sum** S_n = a \frac{r^n - 1}{r - 1}, where n = 6. 3. Calculate the sum S_6 = -3 \frac{4^6 - 1}{4 - 1} = -3 \frac{4096 - 1}{3} = -3 \times 1365 = -4095.

Explanation

1. Identify the first term and common ratio<br /> First term $a = -3$. Common ratio $r = \frac{-12}{-3} = 4$.<br />2. Use the formula for the sum of a geometric series<br /> **Sum** $S_n = a \frac{r^n - 1}{r - 1}$, where $n = 6$.<br />3. Calculate the sum<br /> $S_6 = -3 \frac{4^6 - 1}{4 - 1} = -3 \frac{4096 - 1}{3} = -3 \times 1365 = -4095$.
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