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

Question

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

3
–30
100
–1,000

Answer 1

To determine \( f(3) \) for the given recursive function \( f(n + 1) = -10f(n) \) with the initial condition \( f(1) = 1 \), follow these steps:

1. Calculate \( f(2) \) using the recursive function:
\[
f(2) = -10f(1)
\]
Since \( f(1) = 1 \):
\[
f(2) = -10 \times 1 = -10
\]

2. Calculate \( f(3) \) using the recursive function:
\[
f(3) = -10f(2)
\]
Since \( f(2) = -10 \):
\[
f(3) = -10 \times (-10) = 100
\]

Thus, the value of \( f(3) \) is \( 100 \).

Therefore, the answer is:
\[
\boxed{100}
\]