Question

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 possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

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.

(1, 2), (2, 4), (3, 8), (4, 16)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)

Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)

Part C: Use an explicit formula to find the time she will complete the 10th station. Show your work. (4 points)

Answer 1

part A) recall: in an arithmetic sequence, the same quantity (d) is added/subtracted for each subsequent value
in a geometric series, the same quantity (r) is multiplied/divided to get each subsequent value

so looking at the range values: 2, 4, 6, 8, 16 - what's the pattern, arithmetic or geometric?

Answer 2

part B) recall: a recursive formula gives you an initial value a1 and tells you to get the next term a_(n+1) by either multiplying/dividing or adding/subtracting the previous value a_(n) by either (d), or (r) as appropriate

in your case, the initial range value is 2, and each new value is generated by multiplying the previous value by 2 - how would you write this as a recursive formula? once you have the formula, use it to calculate the y-value for x = 5

Answer 3

part C) recall: an explicit formula will tell you how to get any term a_n in a sequence based on its position n

for geometric sequences, the general form is a_n = a_1 * r^(n-1), fill in the appropriate a_1 and r from the problem. then let n = 10 and calculate a_n