Question

Instructions: Given one form of a sequence, write the other form.

Answer 1

The Solution:

Given:

`a_n=a_(n-1).-6`

Required:

To find the recursive formula for the sequence.

The recursive formula for a geometric sequence is:

`a_n=a_1.r^(n-1)`

From the given formula, we can find r as below:

`\begin{gathered} a_n=a_(n-1).-6 \\ \\ a_n=(-6)a_(n-1) \\ \\ \text{ Divide both sides by }a_(n-1) \\ \\ -6=(a_n)/(a_(n-1))=r \\ \\ r=-6 \end{gathered}`

Recall:

`a_1=-4\text{ \lparen given\rparen}`

So, the explicit form of the recursive formula is: