Chapter 5.6, Problem 48E

To determine

To calculate: The next three terms for the arithmetic sequence $-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2},\dots$ .

Answer to Problem 48E

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

Explanation of Solution

Given information:

The arithmetic sequence $-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2},\dots$ .

Formula used:

A sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

Calculation:

Consider the arithmetic sequence $-\frac{3}{2},-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2},\dots$ .

Recall that a sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

Compute the difference between the consecutive terms,

  $\begin{array}{c}{a}_2-a_1=-\frac{1}{2}+\frac{3}{2}\\ =1\end{array}$

And

  $\begin{array}{c}{a}_3-a_2=\frac{1}{2}+\frac{1}{2}\\ =1\end{array}$

Therefore, common difference is $1$ .

Now, sixth term is,

  $\begin{array}{c}{a}_6=a_5+1\\ =\frac{5}{2}+1\\ =\frac{7}{2}\end{array}$

Now, seventh term is,

  $\begin{array}{c}{a}_7=a_6+1\\ =\frac{7}{2}+1\\ =\frac{9}{2}\end{array}$

And, eight term is,

  $\begin{array}{c}{a}_8=a_7+1\\ =\frac{9}{2}+1\\ =\frac{11}{2}\end{array}$

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