Answer:
(a) s = 33.75
Step-by-step explanation:
You want the sum of the infinite geometric series that begins 21 +9 +3.86 +....
Estimate
The ratio of the first two terms is 9/21 = 3/7. This is a value less than 1, so you know the series converges. The first two terms have a total of 21+9 = 30, so you know the sum is more than 30 and last two answer choices are incorrect.
Of the available answer choices, the most likely answer is 36.75.
Calculation
The formula for the sum of an infinite series with first term a1 and common ratio r is ...
S = a1/(1 -r)
Here, the first term is 21 and the ratio is 9/21 = 3/7, so that sum is ...
S = 21/(1 -3/7) = 21·7/4 = 33.75
The sum of the series is 33.75.
