\begin{cases}d(1)=8\\\\

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

1 answer

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

\[ \boxed{200} \]