Question

Show that there is no A.P. which consists of only distinct prime numbers.

Answer 1

If you show the smallest prime numbers then it will be

2,3,5....

we already know In A.P., a2-a1 should be equal to a3-a2

but in this case

3-2=1 is not equal to 5-3=2. 

∴ this is not an A.P

Answer 2

Heya,


Prime numbers:- 2,3,5,7,11...........................

We know that when there is an AP they have common difference. 

But here,

a2-a1
3-2=1

a3-a2
5-3= .

Therefore they do not have common difference thus there is no AP.

Hope it helps u..............