Question

The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 42 and the common ratio is three fourths. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Answer 1

Since this is the formula for the infinite geometric series with
a1 = 42
r = 3/4

Solution will be

sum = 42 / 1-3/4
sum = 42 / 0.25
sum = 168

Therefore, the total is 168

Answer 2

Answer: the answer is D

Step-by-step explanation: We can immediately eliminate options A and B because they aren’t even formatted properly. The common ratio(3/4) ALWAYS comes after a_1 which in this case was 42. That leaves us with C and D. Now, for series to be divergent, the common ratio(number in parentheses) HAS to be GREATER than one. Since this equation has 3/4 or .75 in the parentheses it is NOT divergent. That leaves us with answer choice D, and the answer is 168. My friend above explains how to get to that answer. Thanks and please rate.