Question

A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is –4. What is the next term in the sequence?

Answer 1

The given sequence is defined recursively by the formula \( f(n + 1) = f(n) + 3 \), and the first term of the sequence is \( f(1) = -4 \).

To find the next term in the sequence, we substitute \( f(1) \) into the recursive formula:

\[ f(2) = f(1) + 3 \]

Given \( f(1) = -4 \), we have:

\[ f(2) = -4 + 3 \]
\[ f(2) = -1 \]

So, the next term in the sequence is \( -1 \).