show that a-b and a+b are consecutive terms of an ap

We need to show that a-b &a+b are consecutive terms of an ap

Now, let a1=a-b

& Common difference =b

Then a2 =a1+ common difference

a2=a-b+b

a2=a

a3 = a2 +common difference

a3= a+ b

Hence from above result 

we can prove that a-b& a+b are consecutive terms of an ap.

Hope it helps.

 

The question is dumb and wrong, because any two terms can never decide the type of sequence. Any two random terms are not only in Ap, they are also in gp, hp, agp etc. So check your question and post again