Question

5) Find
\[d(5)\] in the sequence given by

\[\begin{cases}d(1)=2\\\\
d(n)=d(n-1)+0.4
\end{cases}\]
\[d(5)=\]

Answer 1

To find \( d(5) \) in the given sequence, we start with the initial condition and the recursive relation:

1. **Starting point:**
\[
d(1) = 2
\]

2. **Using the recursive formula:**
\[
d(n) = d(n-1) + 0.4
\]

Now we will compute \( d(2) \), \( d(3) \), \( d(4) \), and \( d(5) \).

- **Calculate \( d(2) \):**
\[
d(2) = d(1) + 0.4 = 2 + 0.4 = 2.4
\]

- **Calculate \( d(3) \):**
\[
d(3) = d(2) + 0.4 = 2.4 + 0.4 = 2.8
\]

- **Calculate \( d(4) \):**
\[
d(4) = d(3) + 0.4 = 2.8 + 0.4 = 3.2
\]

- **Calculate \( d(5) \):**
\[
d(5) = d(4) + 0.4 = 3.2 + 0.4 = 3.6
\]

Thus, the value of \( d(5) \) is
\[
\boxed{3.6}
\]