Chapter 4, Problem 28CR

To determine

To find:An explicit formula that represents the same sequence as the recursive formula $A(n)=A(n-1)+3;A(1)=4$ .

Answer to Problem 28CR

  $A(n)=4+(n-1)3$

Explanation of Solution

Given information: $A(n)=A(n-1)+3;A(1)=4$

Calculation: $A(1)=4$ and the common difference is $d=3$ .

The general form of an explicit formula is,

  $A(n)=A(1)+(n-1)d$

Substituting $A(1)=4$ and $d=3$ ,

  $\begin{array}{l}A(n)=A(1)+(n-1)d\\ \Rightarrow A(n)=4+(n-1)3\end{array}$

The explicit formula is $A(n)=4+(n-1)3$ .