Question

If p-1,p 3,3p-1 are in ap then fimd the value of p

Answer 1

If a,b,c are in AP ,then b-a = c-b
                                     
So , 2b =  a+c

Here , a= p-1
           b = 3
           c=3p-1

So, 2*3 = p-1 + 3p-1
6 = 4p - 2
P=2

Answer 2

Let suppose a, b, c are in Arithmetic Progression (AP) , then we know that,  

b-a = c-b

                                     

So here we can say that, 2b =  a+c --) 1

and now,  

1. a= p-1

2. b = p+ 3

3. c=3p-1

So that put b=3, and point 1 and 3 in equation 1 and we will get,  

-->  2*3 = p-1 + 3p-1

--> 6+2p = 4p - 2

8=2p

P=4

So that the value of P is 4