Question

Miguel has started training for a race. The first time he trains, he runs 0.5 mile. Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time. What arithmetic series represents the total distance Miguel has run after he has trained n times?

Answer 1

First answer is C. (0.3+0.2K)

Second one is 15 Times

Explanation:

Answer on EDG hope it helps :)

Answer 2

`0.4n+0.1n^2\ miles`

Explanation:

The first time he trains, he runs 0.5 mile, then the first term of the arithmetic sequence is
`a_1=0.5.`

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
`d=0.2.`

The nth term of the arithmetic sequence can be found using formula

`a_n=a_1+(n-1)d,`

hence

`a_n=0.5+0.2(n-1)\\ \\a_n=0.5+0.2n-0.2\\ \\a_n=0.3+0.2n.`

The total distance after Miguel has trained n times can be found using formula

`S_n=(a_1+a_n)/(2)\cdot n,`

thus, the total distance is

`S_n=(0.5+0.3+0.2n)/(2)\cdot n=(0.8+0.2n)/(2)\cdot n=(0.4+0.1n)n=0.4n+0.1n^2.`