Question

Find the common difference of the sequence shown 1/6,1/3,1/2,2/3,......

Answer 1

Answer:

Common Difference(d) is    

               $d=\frac{1}{6}$

Step-by-step explanation:

Given sequence is :

                 $\frac{1}{6}, \frac{1}{3} ,\frac{1}{2} ,\frac{2}{3} .........$

If a sequence has a constant common difference throughout the sequence, then the sequence is called Arithmetic Progression.

Considering a sequence:

       $a_1,a_2,a_3,a_4..........$

$a_2-a_1=a_3-a_2=a_4-a_3=a_n-a_n_-_1=d$

where 'd' is the common difference of the A.P.

Similarly, finding the common difference of the given sequence.

       

                           $\frac{1}{3} -\frac{1}{6}= \frac{1}{2}- \frac{1}{3}=\frac{2}{3} - \frac{1}{2}=d$

                              $d=\frac{1}{3}-\frac{1}{6}=\frac{(2)(1)-(1)(1)}{6}=\frac{1}{6}$

                                   $d=\frac{1}{6}$

Common Difference(d) is    

               $d=\frac{1}{6}$

Answer 2

Answer:

The common difference is 1/6.