Question

Use the sequence {−1,171,875;−234,375;−46,875;−9375,…} to answer the question.What is the explicit rule that describes the sequence?

Answer 1

Given the sequence:

`\mleft\{-1,171,875;-234,375;-46,875;-9375,\ldots\mright\}`

Each subsequent number can be calculated using a division by 5. Then, the common ratio of the (geometric) sequence is 1/5, and the initial value is −1,171,875. The explicit rule of the sequence is:

`\begin{gathered} a_n=a_0\cdot r^(n-1) \\ a_0=-1,171,875 \\ r=(1)/(5) \\ \\ \therefore a_n=-1,171,875\cdot((1)/(5))^(n-1) \end{gathered}`