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A sequence is defined by the recursive function f(n + 1) = –10f(n).

If f(1) = 1, what is f(3)?

3
–30
100
–1,000

A sequence is defined by the recursive function fn 1 10fn If f1 1 what is f3 3 30 100 1000 class=
A sequence is defined by the recursive function fn 1 10fn If f1 1 what is f3 3 30 100 1000 class=
A sequence is defined by the recursive function fn 1 10fn If f1 1 what is f3 3 30 100 1000 class=
A sequence is defined by the recursive function fn 1 10fn If f1 1 what is f3 3 30 100 1000 class=

Respuesta :

We are given

[tex]f(n+1)=-10f(n)[/tex]

we are given

[tex]f(1)=1[/tex]

At n=1:

we can plug n=1 into formula

[tex]f(1+1)=-10f(1)[/tex]

[tex]f(2)=-10f(1)[/tex]

[tex]f(2)=-10*1[/tex]

[tex]f(2)=-10[/tex]

At n=2:

we can plug n=2 into formula

[tex]f(2+1)=-10f(2)[/tex]

[tex]f(3)=-10f(2)[/tex]

[tex]f(3)=-10*-10[/tex]

[tex]f(3)=100[/tex]................Answer

A function assigns the value of each element of one set to the other specific element of another set. The value of f(3) is 100.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As the recursive function is given to us, f(n + 1) = –10f(n), also the value of f(1)=1 , therefore, the value of f(2) can be written as,

[tex]f(n + 1) = -10f(n)\\\\f(1 + 1) = -10f(1)\\\\f(2)= -10 \times 1\\\\f(2)=-10[/tex]

Now, the value of f(3) can be written as,

[tex]f(n + 1) = -10f(n)\\\\f(2 + 1) = -10f(2)\\\\f(3)= -10 \times -10\\\\f(3)= 100[/tex]

Hence, the value of f(3) is 100.

Learn more about Function:

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