Question

a sequence is defined by the formula $f(n + 1) = f(n) - 3$. if $f(4) = 22$, what is $f(1)$?
31
10
13
34

Explanation:

Step 1: Understand the sequence relation

The formula \( f(n + 1)=f(n)-3 \) means each term is 3 less than the previous term. So to find a previous term, we can reverse it: \( f(n)=f(n + 1)+3 \).

Step 2: Find \( f(3) \) from \( f(4) \)

We know \( f(4) = 22 \). Using the reversed formula, for \( n = 3 \), \( f(3)=f(4)+3 \).
\( f(3)=22 + 3=25 \)

Step 3: Find \( f(2) \) from \( f(3) \)

Using the reversed formula again, for \( n = 2 \), \( f(2)=f(3)+3 \).
\( f(2)=25 + 3=28 \)

Step 4: Find \( f(1) \) from \( f(2) \)

Using the reversed formula, for \( n = 1 \), \( f(1)=f(2)+3 \).
\( f(1)=28 + 3=31 \)

Answer:

31