Understanding the Recursive Definition of the Function f(n) and Finding Values Using the Formula

f(1)=6, f(n) = 3*f(n-1) for n ≥ 2

This is a recursive definition for a function f(n)

This is a recursive definition for a function f(n). It states that for the base case, when n is equal to 1, f(1) is equal to 6. And for any other value of n greater than or equal to 2, f(n) is defined as 3 times f(n-1).

To understand how this function works, let’s use the given information to find the values of f(n) for some specific values of n.

Using the recursive definition:
f(1) = 6

For n = 2:
f(2) = 3 * f(2-1) = 3 * f(1) = 3 * 6 = 18

For n = 3:
f(3) = 3 * f(3-1) = 3 * f(2) = 3 * 18 = 54

For n = 4:
f(4) = 3 * f(4-1) = 3 * f(3) = 3 * 54 = 162

And so on.

We can observe a pattern here. Each value of f(n) is obtained by multiplying the previous value of f(n-1) by 3. So, f(n) grows exponentially with respect to n.

In general, we can write the recursive formula as:
f(n) = 3^n * f(1)

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

For example, if we want to find f(6):
f(6) = 3^6 * f(1) = 3^6 * 6 = 729 * 6 = 4374

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

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