Question

Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 yards a day for 21 days.

The explicit formula that models this situation is an = 200 + (n – 1)5.

How far does she sprint on day 21?
A. 300 yards
B. 305 yards
C. 205 yards
D. 221 yards

Answer 1

The correct answer is A) 300 yd.

Using the formula, we have 200 + (21-1)(5) = 200+20(5) = 200+100=300

Answer 2

Solution:

we are given that

Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 yards a day for 21 days.

The explicit formula that models this situation is $a_n = 200 + (n-1)5$

we have been asked to find how far does she sprint on day 21?

Substitute the value of n=21 in the given explicit formula we get

$a_{21} = 200 + (21-1)5$

Simplify we get

$a_{21} = 200 + 20*5$

$a_{21} = 200 + 100$

$a_{21} = 300$

Hence the correct option is A.