Matt has started a car washing business for college each week he washes 3 more cars than he did the week before

Question

Matt started washing 6 cars his first week in business write an explicit formula that can be used to find the number of cars he washed any given week.

A
n
=
6
+
3
(
n
−
1
)
A
n
​
=6+3(n−1)

A
n
=
6
(
3
n
−
1
)
A
n
​
=6(3n−1)

A
n
=
6
+
3
n
A
n
​
=6+3n

A
n
=
3
+
6
(
n
−
1
)
A
n
​
=3+6(n−1)

Answer 1

To find the explicit formula for the number of cars Matt washes in any given week (denoted as \( A_n \)), we note that he starts with 6 cars in the first week and washes 3 more cars than the previous week each week.

1. In the first week (\( n = 1 \)), he washes 6 cars: \[ A_1 = 6 \]

2. In the second week (\( n = 2 \)), he washes: \[ A_2 = 6 + 3 = 9 \]

3. In the third week (\( n = 3 \)), he washes: \[ A_3 = 9 + 3 = 12 \]

You can see that the number of cars washed each week can be represented as:

• In the first week, it’s 6.
• In the second week, it’s \( 6 + 3 \times 1 \).
• In the third week, it’s \( 6 + 3 \times 2 \).

Thus, the general formula for the \( n \)-th week can be expressed as: \[ A_n = 6 + 3(n - 1) \]

So the correct explicit formula is: \[ A_n = 6 + 3(n - 1) \]

This matches with option A.