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, 4), (2, 8), (3, 16), (4, 32)

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

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

Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.

Question

Mathematics

Piper Bowen

24 March, 14:56

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, 4), (2, 8), (3, 16), (4, 32)

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

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

Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.

+4

Answers (1)

Know the Answer?

German Drake · Answer 1

Hello there!

Part A: The data is modeling a geometric sequence since the numbers are multiplying and that can't be measured in an arithmetic sequence.

Part B: Recursive Formula for Geometric Sequence

a1 = 4

a (n) = a (n-1) x 2

Plug 5 in:

a (5) = a (5-1) x 16

a (5) = 64

Part C:

a9 = a1 (r) ^n-1

a9 = 4 (2) ^5

a9 = 4 x 32

a9 = 128