Chapter 4, Problem 30CR

To determine

To find:An explicit formula that represents the same sequence as the recursive formula $A(n)=A(n-1)-1;A(1)=19$ .

Answer to Problem 30CR

  $A(n)=19-(n-1)$

Explanation of Solution

Given information: $A(n)=A(n-1)-1;A(1)=19$

Calculation: $A(1)=19$ and the common difference is $d=-1$ .

The general form of an explicit formula is,

  $A(n)=A(1)+(n-1)d$

Substituting $A(1)=19$ and $d=-1$ ,

  $\begin{array}{l}A(n)=A(1)+(n-1)d\\ \Rightarrow A(n)=19+(n-1)(-1)\\ \Rightarrow A(n)=19-(n-1)(1)\\ \Rightarrow A(n)=19-(n-1)\end{array}$

The explicit formula is $A(n)=19-(n-1)$ .