Answered

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A sequence is defined by the recursive function

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

If [tex]\( f(1) = 1 \)[/tex], what is [tex]\( f(3) \)[/tex]?

A. 3
B. -30
C. 100

Sagot :

GinnyAnswer
Sure, let's work through this step-by-step.

1. Initial Condition:
We are given that [tex]\( f(1) = 1 \)[/tex].

2. First Iteration:
We need to find [tex]\( f(2) \)[/tex] using the given recursive function [tex]\( f(n+1) = -10 f(n) \)[/tex].

So, for [tex]\( n = 1 \)[/tex]:
[tex]\[ f(2) = -10 \cdot f(1) \][/tex]
Substituting [tex]\( f(1) = 1 \)[/tex]:
[tex]\[ f(2) = -10 \cdot 1 = -10 \][/tex]

3. Second Iteration:
Next, we need to find [tex]\( f(3) \)[/tex] using the recursive function [tex]\( f(n+1) = -10 f(n) \)[/tex].

So, for [tex]\( n = 2 \)[/tex]:
[tex]\[ f(3) = -10 \cdot f(2) \][/tex]
Substituting [tex]\( f(2) = -10 \)[/tex]:
[tex]\[ f(3) = -10 \cdot (-10) = 100 \][/tex]

Therefore, [tex]\( f(3) = 100 \)[/tex].
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