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 f(n + 1)=-10f(n). if f(1)=1, what is f(3)? 3 -30 100 -1,000
Answer
Answer:
C. 100
Explanation:
Step1: Find f(2)
Given (f(n + 1)=- 10f(n)) and (f(1) = 1). Let (n = 1), then (f(2)=-10f(1)). Substitute (f(1)=1) into the equation, we get (f(2)=-10\times1=-10).
Step2: Find f(3)
Let (n = 2) in (f(n + 1)=-10f(n)). Then (f(3)=-10f(2)). Substitute (f(2)=-10) into the equation, we have (f(3)=-10\times(-10)=100).