Question

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

Answer 1

Answer:

$a_n=80\cdot(\frac{-1}{4})^{n-1}$

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:

$a_n=80\cdot(\frac{-1}{4})^{n-1}$

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

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

Therefore, the answer is:

$a_n=80\cdot(\frac{-1}{4})^{n-1}$