Question

find the value of P, if the number x,2x+p,3x+6 are the three conjuctive terms of an arithmetic progestion

Answer 1

given x, 2x+p, 3x+6 is in arithmetic progression
a = x , d₁ = a₂-a₁ = 2x+p-x
                       d₁= x+p
 d₂ = a₃-a₂ = 3x+6-2x-p
                = x-p+6
 in an AP, d₁ = d₂
       x+p = x-p+6
        x+p-x+p = 6
       2p = 6
         p = 3

Answer 2

x , 2x+p , 3x+6 are in A.P
so we know that ,
          t₂ = (t₁+t₃)/2
or,      2x+p = (x+3x+6)/2
or,      2x+p = 2(2x+3)/2
or,        p = 2x+3-2x
therefore p = 3