Question

\begin{cases}d(1)=8\\\\
d(n)=d(n-1)\cdot (-5)
\end{cases}
What is the \[3^{\text{rd}}\] term in the sequence?

Answer 1

We are given a recursive definition for the sequence \( d(n) \):

\[
d(1) = 8
\]
\[
d(n) = d(n-1) \cdot (-5) \quad \text{for } n > 1
\]

We need to find the third term \( d(3) \).

First, we calculate \( d(2) \):

\[
d(2) = d(1) \cdot (-5) = 8 \cdot (-5) = -40
\]

Next, we calculate \( d(3) \):

\[
d(3) = d(2) \cdot (-5) = -40 \cdot (-5) = 200
\]

Thus, the third term in the sequence is

\[
\boxed{200}
\]