A scooter (small motorcycle) is bought at a price of $9,000. It loses 14% of its value very year. Express this scenario as a sequence recursively and explicitly (provide its general term).

 Let's denote the initial value of the scooter as \( V_0 \), which is $9,000. And let \( V_n \) denote the value of the scooter after \( n \) years.

First, we define the recursive formula, which expresses the value of the scooter after \( n \) years in terms of its value in the previous year \( n-1 \).

Since the scooter loses 14% of its value each year, it retains 86% of its value from the previous year (100% - 14% = 86%). Expressed as a decimal, 86% is 0.86.

The recursive formula for \( V_n \), the value after \( n \) years, is:

\( V_n = 0.86 \cdot V_{n-1} \), for \( n \geq 1 \)

With the initial condition:

\( V_0 = 9000 \) (the initial value of the scooter)

Now, for the explicit formula, which gives the value of the scooter after \( n \) years directly, we recognize that the depreciation compounds each year.

The explicit formula for \( V_n \) is:

\( V_n = V_0 \cdot 0.86^n \)

Plugging in the initial value of the scooter:

\( V_n = 9000 \cdot 0.86^n \)

This explicit formula allows us to calculate the value of the scooter after any given number of years without having to iterate through every single year.