Question

A sequence is defined by the recursive function of f(n+1)=-10f(n). If f(1)=1, what is f(3)?

Answer 1

f(1)=1
f(2)=-10f(1)=-10(1)=-10
f(3)=-10f(2)=-10(-10)=100

Answer 2

f(3) = 100.

Explanation:

Given: f(n+1) = -10 f(n). If f(1)=1,

To find : A sequence is defined by the recursive function.find f(3)

Solution : we have given

f(n+1) = -10 f(n). If f(1)=1,

For n = 1.

F(1+1) = - 10 f( 1) .

Plug the value of f(1) = 1

f(2) = - 10 * 1.

f(2) = - 10.

Then , n = 2.

f(2 + 1) = -10 f( 2) .

Plug f(2) = - 10 .

f(3) = - 10 ( -10) .

f(3) = 100.

Therefore, f(3) = 100.