Recursive Definition and Calculation of f(n) with Example Values | Math Content

f(0) = 9 , f(n) = f(n-1)/3for n ≥ 1

To find the value of f(1), we can use the given recursive definition:

f(n) = f(n-1)/3 for n ≥ 1

Since we’re looking for f(1), we can substitute n = 1 into the definition:

f(1) = f(1-1)/3
f(1) = f(0)/3

We are given that f(0) = 9, so substituting this value:

f(1) = 9/3
f(1) = 3

Therefore, f(1) = 3

To find the value of f(1), we can use the given recursive definition:

f(n) = f(n-1)/3 for n ≥ 1

Since we’re looking for f(1), we can substitute n = 1 into the definition:

f(1) = f(1-1)/3
f(1) = f(0)/3

We are given that f(0) = 9, so substituting this value:

f(1) = 9/3
f(1) = 3

Therefore, f(1) = 3.

To find the value of f(2), we can again use the recursive definition:

f(n) = f(n-1)/3 for n ≥ 1

Substituting n = 2:

f(2) = f(2-1)/3
f(2) = f(1)/3

We have already found the value of f(1) to be 3. Substituting this value:

f(2) = 3/3
f(2) = 1

Therefore, f(2) = 1.

Continuing this pattern, we can find the values of f(3), f(4), and so on. Each subsequent value of f(n) will be one-third of the previous value.

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