Question

3) Find
\[b(4)\] in the sequence given by

\[\begin{cases}b(1)=-5\\\\
b(n)=b(n-1)+9
\end{cases}\]
\[b(4)=\]

Answer 1

To find \( b(4) \) in the given sequence, we start with the initial condition and the recursive rule provided:

\[
\begin{cases}
b(1) = -5 \\
b(n) = b(n-1) + 9
\end{cases}
\]

We'll compute the subsequent terms step by step:

1. **Calculate \( b(2) \):**
\[
b(2) = b(1) + 9 = -5 + 9 = 4
\]

2. **Calculate \( b(3) \):**
\[
b(3) = b(2) + 9 = 4 + 9 = 13
\]

3. **Calculate \( b(4) \):**
\[
b(4) = b(3) + 9 = 13 + 9 = 22
\]

Thus, the value of \( b(4) \) is

\[
\boxed{22}
\]