Question

The total annual spending by tourists in a resort city is $450 million. Approximately 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on. Write the geometric series that gives the total amount of spending generated by the $450 million and find the sum of the series.

Answer 1

G.P. is, 450, 360, 288, 230.4,......

The sum is 2250.

Explanation:

Given,

The first total spending in the resort city = $ 450 million,

Also, 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on.

Thus, there is a G.P. that represents the given situation,

450, 360, 288, 230.4,......

Which is an infinite geometric series having first term, a = 450,

Common ratio, r = 0.8,

Hence, the sum of the series,

`S_n=(a)/(1-r)`

`=(450)/(1-0.8)`

`=(450)/(0.2)`

`=2250`