Chapter 4.7, Problem 34PPE

To determine

Tofind:a recursive formula for the sequence $2.3,2.8,3.3,3.8,\mathrm{......}$ .

Answer to Problem 34PPE

Recursive formula: $A\left(n\right)=A\left(n-1\right)+0.5;A\left(1\right)=2.3$

Explanation of Solution

Given sequence: $2.3,2.8,3.3,3.8,\mathrm{......}$

Calculation:

The first term of the sequence is $A\left(1\right)=2.3$

Since the each term of given sequence after the first term is obtained by adding the previous one by 0.5, therefore given sequence is an arithmetic sequence and common difference is $d=0.5$

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

  $A\left(n\right)=A\left(n-1\right)+0.5;A\left(1\right)=2.3$