Chapter 7, Problem 4SGR

To determine

To fill: the blank in the given statement.

Explanation of Solution

Given information:

Consider “ $a_1=4,a_n=3a_{n-1}-12,n\ge 2$ is $a(n)$ __________ for the sequence

  $4,-8,-20,-32,\mathrm{..}$____________ ”

Explanantion:

Consider $4,-8,-20,-32,\mathrm{..}$

  $\begin{array}{l}{a}_1=4\\ a_2=-8=4-12=a_1-12\\ a_3=-20=-8-12=a_2-12\\ ;\\ ;\\ a_n=a_{n-1}-12\end{array}$

Then, the recursive formula is $a_1=4,a_n=a_{n-1}-12;n\ge 2$ .

Hence, the blank is filled with the term not recursive formula.