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? \boxed{} show calculator

Explanation:

Step1: Find the second term

To find the second term \( d(2) \), we use the recursive formula \( d(n) = d(n - 1) \cdot (-5) \) with \( n = 2 \). So we substitute \( n - 1=1 \) (since \( n = 2 \)) and we know \( d(1)=8 \). Then \( d(2)=d(1)\cdot(-5)=8\times(-5)= - 40 \)

Step2: Find the third term

To find the third term \( d(3) \), we use the recursive formula again with \( n = 3 \). So we substitute \( n - 1 = 2 \) and we know \( d(2)=-40 \) from step 1. Then \( d(3)=d(2)\cdot(-5)=(-40)\times(-5)=200 \)

Answer:

\( 200 \)