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

f(0) = 9, f(n) = f(n-1) +3for n ≥ 1

To find the value of f(n) for any given values of n using the recursive formula, we can begin by substituting the given initial value of f(0) = 9 into the formula

To find the value of f(n) for any given values of n using the recursive formula, we can begin by substituting the given initial value of f(0) = 9 into the formula.

f(0) = 9

Next, we can use the recursive formula f(n) = f(n-1) + 3 to calculate f(1).

f(1) = f(0) + 3
= 9 + 3
= 12

So, f(1) = 12.

Continuing this process, we can find f(2) using f(1).

f(2) = f(1) + 3
= 12 + 3
= 15

Therefore, f(2) = 15.

We can continue this process to find f(n) for any given value of n. Each time, we use the previous value of f(n-1) and add 3 to it.

For example, to find f(3):

f(3) = f(2) + 3
= 15 + 3
= 18

Similarly, to find f(4):

f(4) = f(3) + 3
= 18 + 3
= 21

And so on.

In general, using the recursive formula f(n) = f(n-1) + 3, we can find the value of f(n) by repeatedly adding 3 to the previous value of f(n-1). The initial value f(0) = 9 is given.

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