Question

Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16

Answer 1

Question:

Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16

The numbers are given below as

`-34,-28,-22,-16`

Concept:

Define an arithmetic sequence

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The general form of an arithmetic sequence is given below as

`\begin{gathered} a_n=a_1+(n-1)d \\ a_1=first\text{ }term \\ n=number\text{ of terms} \\ d=common\text{ difference} \end{gathered}`

To check if they have a common difference, we will use the formulas below

`\begin{gathered} d=a_2-a_1=-28-(-34)=-28+34=6 \\ d=a_3-a_2=-22-(-28)=-22+28=6 \\ d=a_4-a_3=-16-(-22)=-16+22=6 \end{gathered}`

Hence,

Since the sequence has a common difference,

It is therefore an ARITHMETIC SEQUENCE

Their common difference is

`\Rightarrow6`