Chapter 4, Problem 27CCSR

a.

To determine

To find:Whether the sequence is an arithmetic sequence.

Answer to Problem 27CCSR

The sequence is an arithmetic sequence.

Explanation of Solution

Given information: $-3.2,-2.4,-1.6,-0.8,\mathrm{...}$

Calculation:

Difference between 2nd term and 1st term $=-2.4-(-3.2)=-2.4+3.2=0.8$

Difference between 3rd term and 2nd term $=-1.6-(-2.4)=-1.6+2.4=0.8$

Difference between 4th term and 3rd term $=-0.8-(-1.6)=-0.8+1.6=0.8$

Since, the sequence has a common difference 0.8 the sequence is arithmetic.

b.

To determine

To find:The next three terms of the sequence.

Answer to Problem 27CCSR

The next three terms of the sequence are $0,0.8,1.6$ .

Explanation of Solution

Given information: $-3.2,-2.4,-1.6,-0.8,\mathrm{...}$

Calculation:

The next three terms of the sequence are,

  $\begin{array}{l}-0.8+0.8=0\\ 0+0.8=0.8\\ 0.8+0.8=1.6\end{array}$

c.

To determine

To find:A recursive formula for the sequence.

Answer to Problem 27CCSR

The recursive formula is $A(n)=A(n-1)+0.8$ , where $A(1)=-3.2$ .

Explanation of Solution

Given information: $-3.2,-2.4,-1.6,-0.8,\mathrm{...}$

Calculation:

The common difference of the arithmetic sequence is $d=0.8$

  $\begin{array}{l}A(1)=-3.2\\ A(2)=A(1)+0.8=-3.2+0.8=-2.4\\ A(3)=A(2)+0.8=-2.4+0.8=-1.6\\ A(4)=A(3)+0.8=-1.6+0.8=-0.8\\ A(n)=A(n-1)+0.8\end{array}$

The recursive formula for the arithmetic sequence is $A(n)=A(n-1)+0.8$ , where $A(1)=-3.2$ .

d.

To determine

To find:Anexplicit formula for the sequence.

Answer to Problem 27CCSR

The explicit formula is $A(n)=-3.2+(n-1)0.8$ .

Explanation of Solution

Given information: $-3.2,-2.4,-1.6,-0.8,\mathrm{...}$

Calculation:

The general form of an explicit formula is,

  $A(n)=A(1)+(n-1)d$

Substituting $A(1)=-3.2$ and $d=0.8$ ,

  $\begin{array}{l}A(n)=A(1)+(n-1)d\\ \Rightarrow A(n)=-3.2+(n-1)0.8\end{array}$

The explicit formula for the arithmetic sequence is $A(n)=-3.2+(n-1)0.8$ .