Question

Write a recursive sequence that represents the sequence defined by the following explicit formula: an = x + 4xn

Answer 1

`\begin{gathered} a_n=a_(n-1)+4x \\ a_1=5x \end{gathered}`

Step-by-step explanation:

Given the sequence defined by the explicit formula:

`a_n=x+4xn`

When n=1:

`\begin{gathered} a_1=x+4x(1)=5x \\ a_1=5x \end{gathered}`

When n=2

`\begin{gathered} a_2=x+4x(2)=9x \\ a_2=9x \end{gathered}`

When n=3

`\begin{gathered} a_3=x+4x(3)=13x \\ a_3=13x \end{gathered}`

We observe that:

`\begin{gathered} 9x-5x=4x \\ 13x-9x=4x \end{gathered}`

This means that to get the next term, we add 4x to the previous term.

Therefore, a recursive formula for the sequence will be:

`\begin{gathered} a_n=a_(n-1)+4x \\ a_1=5x \end{gathered}`