Chapter 4.7, Problem 38PPE

To determine

To find : an explicit formula for the recursive formula $A\left(n\right)=A\left(n-1\right)+12;A\left(1\right)=12$ .

Answer to Problem 38PPE

  $A\left(n+1\right)=12+\left(n-1\right)\left(12\right)$

Explanation of Solution

Given information: The recursive formula for the sequence is $A\left(n\right)=A\left(n-1\right)+12;A\left(1\right)=12$

Calculation:

The first term of given sequence is $A\left(1\right)=12$

We know that the recursive formula for the arithmetic sequence with first term $A\left(1\right)$ and common ratio d is

  $A\left(n\right)=A\left(n-1\right)+d$

Therefore, the common ratio is $d=12$ .

Now, the explicit formula for the arithmetic sequence with first term $A\left(1\right)$ and common ratio d is

  $A\left(n\right)=A\left(1\right)+\left(n-1\right)\left(d\right)$

Thus, explicit formula for given sequence is

  $A\left(n+1\right)=12+\left(n-1\right)\left(12\right)$