The annual spending by tourists in a resort city is 200 million dollars. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the resort city. If this pattern continues, write the geometric series that gives the total amount of spending generated by the 200 million dollars (including the initial outlay of 200 million dollars) and find the sum of the series.
A)The geometric series is $\sum _ { n = 1 } ^ { \infty } 200 ( 75 ) ^ { n + 1 }$ .The sum of the series is $\$$ 800.00 million.
B)The geometric series is $\sum _ { n = 1 } ^ { \infty } 200 ( 0.25 ) ^ { n }$ .The sum of the series is $\$$ 15,000 million.
C)The geometric series is $\sum _ { n = 0 } ^ { \infty } 200 ( 0.75 ) ^ { n }$ .The sum of the series is $\$$ 800.00 million.
D)The geometric series is $\sum _ { n = 0 } ^ { \infty } 200 ( 0.75 ) ^ { n }$ .The sum of the series is $\$$ 15,000 million.
E)The geometric series is $\sum _ { n = 1 } ^ { \infty } 200 ( 25 ) ^ { n + 1 }$ .The sum of the series is $\$$ 150.00 million.

Question

Quizplus · Accepted Answer

The correct geometric series starts with the initial spending of $200 million and multiplies by 0.75 for each subsequent round of spending, starting from the 0th term to account for the initial spending. The sum of an infinite geometric series is calculated using the formula $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = 200$ million and $r = 0.75$, so the sum is $S = \frac{200}{1 - 0.75} = 800$ million dollars.

The Annual Spending by Tourists in a Resort City Is ∑n=1∞200(75)n+1\sum _ { n = 1 } ^ { \infty } 200 ( 75 ) ^ { n + 1 }∑n=1∞​200(75)n+1

The Annual Spending by Tourists in a Resort City Is $\sum _ { n = 1 } ^ { \infty } 200 ( 75 ) ^ { n + 1 }$