Aurora intends to take part in a competition during her school's field day where she must finish tasks at several stations as quickly as she can. She's practicing and timing herself as she completes each station to get ready for the competition. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.&nbsp;(1,3),(2,6),(3,12),(4,24)Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.Part B: Use a recursive formula to determine the time she will complete station 5.Part C: Use an explicit formula to find the time she will complete the 9th station.

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Aurora intends to take part in a competition during her school&#039;s field day where she must finish tasks at several stations as quickly as she can. She&#039;s practicing and timing herself as she completes each station to get ready for the competition. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.&amp;nbsp;(1,3),(2,6),(3,12),(4,24)Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.Part B: Use a recursive formula to determine the time she will complete station 5.Part C: Use an explicit formula to find the time she will complete the 9th station.

stuth1 · Accepted Answer

Aurora is practicing and timing how long it takes her to finish each station. The station number is the x-coordinate, and the amount of time in minutes since the race&#039;s beginning that she spent finishing the task is the y-coordinate.&amp;nbsp;(1,3),(2,6),(3,12),(4,24).(A) Here, y-coordinate have values asa1=3,a2=6,a3=12,a4=24,a5,……anIn the above sequence,a2a1=63=2a3a4=126=2As a result, the above sequence data is modeling a geometric sequence since it adheres to the same common ratio geometric sequence pattern.(B) We know that for a geometric sequence, nth term of sequence having first term a and common ratio r is given as&amp;nbsp;an=arn−1&amp;nbsp;⋯⋯(1)From the given data, x-coordinate corresponds to station number and y-coordinate corresponds to time t.For station5, we need to calculate 5-th term of the sequence given by equation (1).On substituting&amp;nbsp;a=3,r=2,&amp;nbsp;and&amp;nbsp;n=5&amp;nbsp;in equation (1) and using explicit formula to determine the time she will complete station 5 asa5=(3)⋅(2)5−1=(3)⋅(2)4=(3)⋅(16)=48&amp;nbsp;minutesHence, the time she will complete station 5 is 48 minutes.(C)For station 9, we need to calculate&amp;nbsp;9th&amp;nbsp;term of the sequence given by equation (1).On substituting&amp;nbsp;a=3,r=2,&amp;nbsp;and&amp;nbsp;n=5&amp;nbsp;in equation (1) and using explicit formula to determine the time she will complete station 9 asa9=(3)⋅(2)9−1=(3)⋅(2)8=(3)⋅(256)=768&amp;nbsp;minutesHence, the time she will complete station 9 is 768 minutes.

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time po

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