To find \( f(1) \) given the sequence \( f(n+1) = f(n) - 3 \) and \( f(4) = 22 \), we need to work our way backwards from \( f(4) \) to \( f(1) \).
Let's start by working backwards step-by-step:
1. \( f(4) = 22 \)
2. To find \( f(3) \), we use the relationship: \( f(3) = f(4) + 3 \)
\[
f(3) = 22 + 3 = 25
\]
3. To find \( f(2) \), we use the relationship: \( f(2) = f(3) + 3 \)
\[
f(2) = 25 + 3 = 28
\]
4. To find \( f(1) \), we use the relationship: \( f(1) = f(2) + 3 \)
\[
f(1) = 28 + 3 = 31
\]
Thus, \( f(1) = 31 \).
Hence, the correct answer is:
\[
\boxed{31}
\]
A sequence is defined by the formula f(n+1)=f(n)−3. If f(4)=22, what is f(1)?
10
13
31
34
1 answer