Answer:
[tex]0.4n+0.1n^2\ miles[/tex]
Step-by-step explanation:
The first time he trains, he runs 0.5 mile, then the first term of the arithmetic sequence is [tex]a_1=0.5.[/tex]
Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time, then the difference of the arithmetic sequence is [tex]d=0.2.[/tex]
The nth term of the arithmetic sequence can be found using formula
[tex]a_n=a_1+(n-1)d,[/tex]
hence
[tex]a_n=0.5+0.2(n-1)\\ \\a_n=0.5+0.2n-0.2\\ \\a_n=0.3+0.2n.[/tex]
The total distance after Miguel has trained n times can be found using formula
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n,[/tex]
thus, the total distance is
[tex]S_n=\dfrac{0.5+0.3+0.2n}{2}\cdot n=\dfrac{0.8+0.2n}{2}\cdot n=(0.4+0.1n)n=0.4n+0.1n^2.[/tex]
Answer:
First answer is C. (0.3+0.2K)
Second one is 15 Times
Step-by-step explanation:
Answer on EDG hope it helps :)
