Chapter 5.6, Problem 48E

To determine

To find: The next three terms of the arithmetic sequence $-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2},\mathrm{...}$

Answer to Problem 48E

The next three terms of the given arithmetic sequence are $\frac{7}{2},\frac{9}{2},\frac{11}{2}$ .

Explanation of Solution

Given information:

The given arithmetic sequence is $-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2},\mathrm{...}$ .

Calculation:

First term, $a_1=-\frac{3}{2}$

Common difference, $d=-\frac{1}{2}-\left(-\frac{3}{2}\right)=-\frac{1}{2}+\frac{3}{2}=\frac{-1+3}{2}=\frac{2}{2}=1$

nth term of the given arithmetic sequence is

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ a_n=-\frac{3}{2}+\left(n-1\right)\left(1\right)\\ a_n=-\frac{3}{2}-1+n\\ a_n=\frac{2n-5}{2}\end{array}$

First five terms of the arithmetic sequence are given. The next three terms are $a_6,a_7,a_8$ . They are

  $\begin{array}{l}{a}_6=\frac{2\left(6\right)-5}{2}\\ a_6=\frac{7}{2}\\ a_7=\frac{2\left(7\right)-5}{2}\\ a_7=\frac{9}{2}\\ a_8=\frac{2\left(8\right)-5}{2}\\ a_8=\frac{11}{2}\end{array}$