Question

Write a recursive sequence that represents the sequence defined by the following explicit formula: an = 3 - 9(n - 1)

Answer 1

`a_{n\text{ }}=a_{n-1\text{ }}+\text{ 9}`

Here, we want to write the recursive formula from the given eplicit formula

We have the following;

`\begin{gathered} a_1\text{ = 3-9(1-1)} \\ a_1\text{ = 3-0 = 3} \\ \\ a_2\text{ = 3-9(2-1) = 3-9(1); 3-9 = -6} \\ \\ a_3\text{ = 3-9(3-1) = 3-9(2) = -15} \\ \\ a_4\text{ = 3-9(4-1) = 3-9(3) = 3-27 = -24} \end{gathered}`

Thus, we have the recursive formula as;

`a_{n\text{ }}=a_{n-1\text{ }}+\text{ 9}`

We add 9 to the succeeding term to get the preceeding term