## f(0) = 3, f(n) = f(n-1)*9for n ≥ 1

### In the given problem, we are given the value of f(0) as 3, and a recursive formula to find f(n) for n ≥ 1

In the given problem, we are given the value of f(0) as 3, and a recursive formula to find f(n) for n ≥ 1. The recursive formula states that f(n) is equal to f(n-1) multiplied by 9.

To find the value of f(n) for a specific value of n, we can use the recursive formula to work our way up from f(0).

Let’s calculate f(1) using the recursive formula:

f(1) = f(0) * 9

f(1) = 3 * 9

f(1) = 27

Now, let’s calculate f(2) using the recursive formula:

f(2) = f(1) * 9

f(2) = 27 * 9

f(2) = 243

We can continue this process to find the value of f(n) for any positive integer n.

The pattern that arises from the recursive formula is that each term is obtained by multiplying the previous term by 9.

So, the general formula for f(n) in terms of n can be written as:

f(n) = f(n-1) * 9

Using this formula, we can find the value of f(n) for any positive integer n.

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The Recursive Formula for Finding f(n) Using the Initial Value of f(0) = 9 and an Increment of 3