Chapter 6.6, Problem 32E

To determine

To write a recursive rule for an explicit rule $a_n=6n-20$ .

Answer to Problem 32E

A recursive rule of given sequence is $a_1=-14,a_n=a_{n-1}+6.$

Explanation of Solution

Given information:

Given an explicit rule $a_n=6n-20$ .

The given explicit rule $a_n=6n-20$ represents an arithmetic sequence with first term $a_1=6\left(1\right)-20=-14$ and common difference $d=6$ .

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

  $\begin{array}{l}\Rightarrow a_n=a_{n-1}+(6)\\ \therefore a_n=a_{n-1}+6\end{array}$

Hence, a recursive rule of given sequence is $a_1=-14,a_n=a_{n-1}+6.$