QuestionMarika starts sprinting 100 yards and adds 4 yards daily for 21 days. Find her distance on day 21 using $a_{n}=100+(n-1)4$ . Options: A. 200 B. 184 C. 221 D. 180.

Studdy Solution

STEP 1

Assumptions1. Marika starts by sprinting100 yards. . She increases her distance by4 yards each day.
3. The explicit formula that models this situation is $a_{n}=100+(n-1)4$ .
4. We need to find the distance she sprints on day21.

STEP 2

The explicit formula given is $a_{n}=100+(n-1)4$ . This formula is used to calculate the distance Marika sprints on any given day 'n'.

STEP 3

To find the distance she sprints on day21, we substitute $n=21$ into the formula.
$a_{21}=100+(21-1)$

STEP 4

First, we simplify the expression inside the parenthesis.
$a_{21}=100+(20)4$

STEP 5

Next, we multiply20 by4.
$a_{21}=100+80$

STEP 6

Finally, we add100 and80 to find the total distance Marika sprints on day21.
$a_{21}=180$ So, Marika sprints180 yards on day21. The correct answer is D.180 yards.

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QuestionMarika starts sprinting 100 yards and adds 4 yards daily for 21 days. Find her distance on day 21 using $a_{n}=100+(n-1)4$ . Options: A. 200 B. 184 C. 221 D. 180.

Studdy Solution

STEP 1

Assumptions1. Marika starts by sprinting100 yards. . She increases her distance by4 yards each day.
3. The explicit formula that models this situation is $a_{n}=100+(n-1)4$ .
4. We need to find the distance she sprints on day21.

STEP 2

The explicit formula given is $a_{n}=100+(n-1)4$ . This formula is used to calculate the distance Marika sprints on any given day 'n'.

STEP 3

To find the distance she sprints on day21, we substitute $n=21$ into the formula.
$a_{21}=100+(21-1)$

STEP 4

First, we simplify the expression inside the parenthesis.
$a_{21}=100+(20)4$

STEP 5

Next, we multiply20 by4.
$a_{21}=100+80$

STEP 6

Finally, we add100 and80 to find the total distance Marika sprints on day21.
$a_{21}=180$ So, Marika sprints180 yards on day21. The correct answer is D.180 yards.

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QuestionMarika starts sprinting 100 yards and adds 4 yards daily for 21 days. Find her distance on day 21 using an=100+(n−1)4a_{n}=100+(n-1)4an​=100+(n−1)4. Options: A. 200 B. 184 C. 221 D. 180.

Studdy Solution

STEP 1

Assumptions1. Marika starts by sprinting100 yards. . She increases her distance by4 yards each day.3. The explicit formula that models this situation is an=100+(n−1)4a_{n}=100+(n-1)4an​=100+(n−1)4.4. We need to find the distance she sprints on day21.

STEP 2

The explicit formula given is an=100+(n−1)4a_{n}=100+(n-1)4an​=100+(n−1)4. This formula is used to calculate the distance Marika sprints on any given day 'n'.

STEP 3

To find the distance she sprints on day21, we substitute n=21n=21n=21 into the formula.a21=100+(21−1)a_{21}=100+(21-1)a21​=100+(21−1)

STEP 4

First, we simplify the expression inside the parenthesis.a21=100+(20)4a_{21}=100+(20)4a21​=100+(20)4

STEP 5

Next, we multiply20 by4.a21=100+80a_{21}=100+80a21​=100+80

STEP 6

Finally, we add100 and80 to find the total distance Marika sprints on day21.a21=180a_{21}=180a21​=180So, Marika sprints180 yards on day21. The correct answer is D.180 yards.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMarika starts sprinting 100 yards and adds 4 yards daily for 21 days. Find her distance on day 21 using $a_{n}=100+(n-1)4$ . Options: A. 200 B. 184 C. 221 D. 180.

Assumptions1. Marika starts by sprinting100 yards. . She increases her distance by4 yards each day.
3. The explicit formula that models this situation is $a_{n}=100+(n-1)4$ .
4. We need to find the distance she sprints on day21.

The explicit formula given is $a_{n}=100+(n-1)4$ . This formula is used to calculate the distance Marika sprints on any given day 'n'.

To find the distance she sprints on day21, we substitute $n=21$ into the formula.
$a_{21}=100+(21-1)$

First, we simplify the expression inside the parenthesis.
$a_{21}=100+(20)4$

Next, we multiply20 by4.
$a_{21}=100+80$

Finally, we add100 and80 to find the total distance Marika sprints on day21.
$a_{21}=180$ So, Marika sprints180 yards on day21. The correct answer is D.180 yards.