Chapter SH, Problem 3.14EP

To determine

To find the sequence

  $-6,-3,0,3,6\mathrm{......}$

is arithmetic or not.

Answer to Problem 3.14EP

The sequence is the arithmetic sequence.

Explanation of Solution

Given information:

The sequence

  $-6,-3,0,3,6\mathrm{......}$

Formula used:

  $d=a_{next}-a_{previous}$

d is common difference of the arithmetic sequence

where as,

  is like first term in arithmetic sequence

And,

  is like second term in arithmetic sequence

Calculation:

The sequence

  $-6,-3,0,3,6\mathrm{......}$

  $Firstterm,a_1=-6$

  $\text{Second term, }{a}_2=-3$

  $Third\text{ term, }{a}_3=0$

  $Fourth\text{ term, }{a}_4=3$

  $Fifth\text{ term, }{a}_5=6$....

And so on.

Then,

Common difference for first and second term is given below $d=-3-(-6)$

On solving,

  $d=3.$

And, common difference for second and third term is given below

  $d=0-(-3)$

On solving,

  $d=3.$

And, common difference for third and fourth term is given below

  $d=6-3$

On solving,

  $d=3.$

Beacuse common differencs for any two consecutive terms is same.

Hence, the sequence is the arithmetic sequence.