Chapter 9.2, Problem 40E

To determine

To find :The first five terms of the arithmetic sequence defined recursively.

Answer to Problem 40E

The first five terms of the arithmetic sequence are

  $a_1=-1.0,a_2=-0.25,a_3=0.5,a_4=1.25,a_5=2.0$

Explanation of Solution

Given information: $a_3=0.5,a_{n+1}=a_n+0.75$

Calculation:

Given recursive formula for the arithmetic sequence is

  $a_3=0.5,a_{n+1}=a_n+0.75$

By substituting $n=3,4$ in the recursive formula for the arithmetic sequence and by using the previous term, we get

  $\begin{array}{l}{a}_4=a_3+0.75=0.5+0.75=1.25\\ a_5=a_4+0.75=1.25+0.75=2.0\end{array}$

Now, given recursive formula for the arithmetic sequence can also be written as

  $a_3=0.5,a_n=a_{n+1}-0.75$

By substituting $n=2,1$ in the recursive formula for the arithmetic sequence and by using the succeeding term, we get

  $\begin{array}{l}{a}_2=a_3-0.75=0.5-0.75=-0.25\\ a_1=a_2-0.75=-0.25-0.75=-1.0\end{array}$