Answer: Choice D) 5.2 * 10^7
This value is 52 million.
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Explanation:
During the first year, the well produced 50,000 quarts of water per week. Since there are 52 weeks in a year, the well produced 52*50,000 = 2,600,000 quarts in total for that first year alone. This is the initial value 'a'.
The common ratio is r = 1 - 0.05 = 0.95
So we have a geometric sequence with starting term a = 2,600,000 and common ratio r = 0.95
Since -1 < r < 1 is true, we can use the infinite geometric series formula as shown below.
S = a/(1 - r)
S = (2,600,000)/(1-0.95)
S = 52,000,000
S = 5.2 * 10^7 which is choice D
