Question

2, 5/2, 3, 7/3,..Is the following sequence is A.P.? If they are AP find the common difference.

Answer 1

d= 5/2-2= 5-4/2= 1/2
Again. d= 3-5/2= 6-5/2= 1/2
Therfore common difference is 1/2.

Answer 2

Answer:

The given terms are not in A.P. and hence the common difference does not exist for the given set of sequence.  

Step-by-step explanation:

The terms are given :

$2,\frac{5}{2},3,\frac{7}{3},.....\\\\d_1=\frac{5}{2}-2\\\\d_1=\frac{1}{2}\\\\d_2=3-\frac{5}{2}\\\\d_2=\frac{1}{2}\\\\d_3=\frac{7}{3}-3\\\\d_3=-\frac{2}{3}\\\\\text{Now, }d_1=d_2\neq d_3$

Now, for the sequence to be in A.P. the difference between all the consecutive terms must be same. But, in this case the difference is not same.

So, the given terms are not in A.P. and hence the common difference does not exist for the given set of sequence.