find the value of p,if the numbers x, 2x+p and 3x+6 are three consecutive terms of an a.p
Since it is APthe difference of 3x+6 and 2x+p is equal to the difference of 2x+p and x
So 3x+6 -(2x+ p)= 2x+p-x
3 x+6-2x-p= x+ p
X+6-p= x+p
Canceling x on both sides and bringing ps to one side we will have 2p= 6
P=3
To find the value of p, we can set up the equation for an arithmetic progression (a.p.) using the given terms.
In an arithmetic progression, the difference between any two consecutive terms is constant.
So, let's set up the equation using the given terms:
2x + p - x = 3x + 6 - (2x + p)
Rewriting the equation:
x + p = x + 6
From this equation, we can deduce that p = 6.
Therefore, the value of p is 6.