## 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:

Recursive Formula for f(n) in Math | Calculating Values and Finding the General FormulaRecursive Function | Exploring the Definition and Values of f(n) with Examples

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