Chapter 8, Problem 19CR

To determine

To verify: the sequence is arithmetic or not.

Answer to Problem 19CR

The sequence $0,1,3,6,\mathrm{10....}$ is not Arithmetic sequence.

Explanation of Solution

Given information:

The sequence which needs to be verified is as follows.

  $0,1,3,6,\mathrm{10....}$

Formula used:

Common difference of the arithmetic sequence is difference of its two consecutive terms and must be equal for all consecutive terms.

Calculation:

The sequence is as follows.

  $0,1,3,6,\mathrm{10....}$

First term of sequence is $a_1=0$ .

Second term of sequence is $a_2=1$ .

Third term of sequence is $a_3=3$ .

Fourth term of sequence is $a_4=6$ .

Fifth term of sequence is $a_5=10$ .

Calculating common difference

  $a_2-a_1=1-0=1$ ,

  $a_3-a_2=3-1=2$

  $a_4-a_3=6-3=3$

  $a_5-a_4=10-6=4$

As difference $a_2-a_1\ne a_3-a_2\ne a_4-a_3\ne a_5-a_4$ , so the sequence is not arithmetic.

Hence it can be concluded that the sequence $0,1,3,6,\mathrm{10....}$ is not Arithmetic sequence.