Chapter 6.6, Problem 31E

To determine

To write a recursive rule for an explicit rule $a_n=1.5n+3$ .

Answer to Problem 31E

A recursive rule of given sequence is $a_1=4.5,a_n=a_{n-1}+1.5.$

Explanation of Solution

Given information:

Given an explicit rule $a_n=1.5n+3$ .

The given explicit rule $a_n=1.5n+3$ represents an arithmetic sequence with first term $a_1=1.5\left(1\right)+3=4.5$ and common difference $d=1.5$ .

Thus, the recursive rule for an arithmetic sequence is $a_n=a_{n-1}+d$

  $\begin{array}{l}\Rightarrow a_n=a_{n-1}+(1.5)\\ \therefore a_n=a_{n-1}+1.5\end{array}$

Hence, a recursive rule of given sequence is $a_1=4.5,a_n=a_{n-1}+1.5.$