Given:
Ernest's schedule:
[tex]1,1.25,1.5,1.75,.......[/tex]
Denise's schedule:
[tex]1,1.5,2,2.5,........[/tex]
Required:
To calculate the distance we'll be swimming inthe 10th week for each schedule.
Explanation:
The nth term of the arithmetic sequence can be calculated by using the formula,
[tex]a_n=a+(n-1)d[/tex]
Now consider the Ernest's schedule:
[tex]1,1.25,1.5,1.75,.....[/tex]
Here,
[tex]\begin{gathered} a=1 \\ d=0.25 \\ n=10 \end{gathered}[/tex]
Therefore, the distance we'll be swimming inthe 10th week for the Ernest's schedule is,
[tex]\begin{gathered} =1+(10-1)0.25 \\ =1+(9)0.25 \\ =1+2.25 \\ =3.25 \end{gathered}[/tex]
Now consider the Denise's schedule:
[tex]1,1.5,2,2.5,......[/tex]
Here,
[tex]\begin{gathered} a=1 \\ n=10 \\ d=0.5 \end{gathered}[/tex]
Therefore, the distance we'll be swimming inthe 10th week for the Deniese's schedule is,
[tex]\begin{gathered} =1+(10-1)0.5 \\ =1+(9)0.5 \\ =1+4.5 \\ =5.5 \end{gathered}[/tex]
So, the Deniese plan is better.
Final Answer:
Deniese plan is better.
