contestada

Consider this function in recursive form.

f(1) = -3

f(n) = 3f(n − 1); n 2 2

Select the equivalent explicit function for n 2 1.

f(n) = -3(n)

o f(n) = -3(n - 1)

• f(n) = -3(3)"

o f(n) = -3(3)(n-1)

Respuesta :

Answer:

Step-by-step explanation:

We are given that f(1) = -3. We will calculate the first terms and check for a pattern.

f(2) = 3*f(1) = -3*3 = -9

f(3) = 3*f(2) = -3*3*3 = -27

f(4) = 3*f(3) = -3*3*3*3 = -81

So, in this case, we see that to get the value at n, we must multiply 3 times itself a total of n times and the multiply it by -1. Thus, the explicit formula is

[tex]f(n) = -3^{n}[/tex]. We can easily check that this function satisfies the values we calculated.

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