Chapter 4.7, Problem 33PPE

To determine

To find : a recursive formula for the sequence $13,10,7,4,,\mathrm{.......}$

Answer to Problem 33PPE

Recursive formula: $A\left(n\right)=A\left(n-1\right)-3;A\left(1\right)=13$

Explanation of Solution

Given sequence: $13,10,7,4,,\mathrm{.......}$

Calculation:

The first term of the sequence is $A\left(1\right)=13$

Since the each term of given sequence after the first term is obtained by adding the previous one by $-3$ , therefore given sequence is an arithmetic sequence and common difference is $d=-3$

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

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

By substituting the value of d, we get the recursive formula for the given sequence

  $A\left(n\right)=A\left(n-1\right)-3;A\left(1\right)=13$