Yohanna is conditioning all summer to prepare for her high school's varsity soccer team tryouts. She is incorporating walking planks into her daily workout training plan. Every day, she will complete four more walking planks than the day before. Part A If she starts with five walking planks on the first day, write an explicit formula that can be used to find the number of walking planks Yohanna completes on any given day. Part B How many walking planks will Yohanna do on the 12th day? A 49 B 53 C 59 D 64

Accepted Solution

Part A
The number of walking planks is given by the series
5, 9, 13, ..., 
This is an arithmetic series with
a = 5, the first term
d = 4, the common difference

On the n-th day, the number of walking planks is
[tex]a_{n} = 5 + 4(n-1)[/tex]

Answer: [tex]a_{n} = 5 +4(n-1)[/tex]

Part B
On the 12-th day, the number of walking planks is
[tex]a_{12} = 5 +4(12-1) = 5 +44 = 49[/tex]

Answer: A. 49