Question

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

Answer 1

The common difference is 1/6.

Answer 2

Common Difference(d) is

`d=(1)/(6)`

Explanation:

Given sequence is :

`(1)/(6), (1)/(3) ,(1)/(2) ,(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.

`(1)/(3) -(1)/(6)= (1)/(2)- (1)/(3)=(2)/(3) - (1)/(2)=d\\`

`d=(1)/(3)-(1)/(6)=((2)(1)-(1)(1))/(6)=(1)/(6)`

`d=(1)/(6)`

Common Difference(d) is

`d=(1)/(6)`