Chapter 9.2, Problem 5E

To determine

To find whether the sequence $1,2,4,8,16,...$ is arithmetic and if so, then find its common difference.

Answer to Problem 5E

The sequence $1,2,4,8,16,...$ is not arithmetic.

Explanation of Solution

Given information :

Let the sequence be $1,2,4,8,16,...$ .

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:

  $\begin{array}{l}{a}_2-a_1=2-1=1\\ a_3-a_2=4-2=2\\ a_4-a_3=8-4=4\end{array}$

Since, $a_2-a_1\ne a_3-a_2\ne a_4-a_3$ , therefore the sequence is not arithmetic.