Chapter 8, Problem 5QC

To determine

To calculate: To find in which week will Becky first jog more than $30$ minutes

Answer to Problem 5QC

Becky will first jog more than $30$ weeks in 5^th week.

Explanation of Solution

Given information: Becky started an exercise program that calls for $12$ minutes of jogging each day during the first week. Each week after, Becky increases the time she jogs by $5$ minutes

Formula Used:

Term: In a sequence, each number is referred to as a term

Term Number: In a sequence, the position of the given term is referred to as term number.

When the difference between the consecutive terms of a sequence is common, then the sequence is an arithmetic sequence.

Nth number of arithmetic sequence is given as

  $t_n=a+\left(n-1\right)d$

Calculation:

Given that Becky started an exercise program that calls for $12$ minutes of jogging each day during the first week.

Thus, first term of sequence is $12$

Each week after, Becky increases the time she jogs by $5$ minutes

Thus, Sequence is given as follow:

  $12,17,22,27,\mathrm{32...}$

Here, the first term of the sequence is $a=12$

From the above sequence, it is observed that 32 is the $5th$ term number.

This means, Becky first jog for more than $30$ minutes in 5^th week.

Conclusion:

Hence, Becky will first jog more than $30$ weeks in 5^th week.