Question

erza is training for a track race. He starts by sprinting 100 yards. he gradually increases his distance, adding 5 yards a day for 21 days. Which explicit formula models this situation? A. an=100 + (n-1)21 B. an=100 + (n-1)5 C. an=5 + (n-1)100 D. an=21 + (n-1)5

Answer 1

Option B.

Explanation:

It is given that erza is training for a track race. He starts by sprinting 100 yards. he gradually increases his distance, adding 5 yards a day for 21 days. So, the required sequence is

100, 105, 110, 115, ...

It is an AP. Here,

First term = 100

Common difference = 5

Explicit formula for an AP is

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

where,
`a_1` is first term and d is common difference of the AP.

Substitute
`a_1=100\text{ and }d=5` in the above formula.

`a_n=100+(n-1)5`

Therefore, the required explicit formula is
`a_n=100+(n-1)5`.

Hence, option B is correct.