Question

Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 years a day for 21 days. Which explicit formula models this situation?

Answer 1

Freya begins started with 200 yards.

Freya then increased her distance by adding five yards a day for two days.

x = 200 + (n - 1)5.

[x = The distance Freya sprints on day 21]

x = 200 + (21 - 1)5

x = 200 + (20) 5 = 300 yards

Answer 2

`a _ n = 200 + ( n - 1 ) 5`

Explanation:

We are given that initially, Freya started with sprinting 200 yards and then gradually increased the distance by adding 5 yards a day for 21 days.

So our initial value for distance is
`a_1=200`

and since she keeps on adding 5 yards everyday to her distance so this will be our common difference.

Therefore, the explicit formula will be:

`a_n=200+(n-1)5`