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?

Step-by-step explanation:

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

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

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

hence

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

thus, the total distance is

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

she gotta workk that a 2

step-by-step explanation: