Question

Th Write an explicit formula for an, then term of the sequence 80, -20,5.....

Answer 1

`a_n=80\cdot((-1)/(4))^(n-1)`

Step-by-step explanation:

We can see that 20 is equal to 80 divided by 4 and 5 is equal to 20 divided by 4. Additionally, the sign change for every term. So, the explicit formula for an is:

`a_n=80\cdot((-1)/(4))^(n-1)`

So, we can prove that this equation applies for the first 3 terms as:

`\begin{gathered} a_1=80\cdot((-1)/(4))^(1-1)=80 \\ a_2=80\cdot((-1)/(4))^(2-1)=-20 \\ a_3=80\cdot((-1)/(4))^(3-1)=5 \end{gathered}`

Therefore, the answer is:

`a_n=80\cdot((-1)/(4))^(n-1)`