Chapter 3.6, Problem 10PPS

To determine

To find:Whether the sequence $-10,-7,-4,1,...$ is an arithmetic sequence.

Answer to Problem 10PPS

No. The sequence $-10,-7,-4,1,...$ is not arithmetic.

Explanation of Solution

Given information:

The terms of the sequence be defined as $a_1=-10,a_2=-7,a_3=-4,a_4=1,\dots ,$

Concept used:

In a sequence $a_1,a_2,a_3,a_4,\dots \dots ,a_n,\dots$ if the difference between the consecutive terms are the same then it is defined as Arithmetic Sequence.

Here, $a_2-a_1=a_3-a_2=a_4-a_3=\dots \dots =d.$ The number $d$ is the common difference of the arithmetic sequence.

Calculations:

Calculate the difference of the consecutive terms:

  $\begin{array}{l}{a}_2-a_1=-7-\left(-10\right)=3\\ a_3-a_2=-4-\left(-7\right)=3\\ a_4-a_3=1-\left(-4\right)=5\\ ⋮\end{array}$

And so on.

Since, the difference between the consecutive terms is not same, that is $a_2-a_1=a_3-a_2\ne a_4-a_3\dots$ , therefore the sequence is not arithmetic.