Find the value of '$p$' if the numbers $x,\ 2x+p,\ 3x+p$ are three successive terms of the A.P.
Given: Numbers $x,\ 2x+p,\ 3x+p$ are three successive terms of the A.P.
To do: To find the value of '$p$'.
Solution:
As given numbers $x,\ 2x+p,\ 3x+p$ are three successive terms of the A.P.
As known $b-a=c-b$, if $a,\ b,\ c$ are in A.P.
$\Rightarrow ( 2x+p)-x=( 3x+p)-( 2x+p)$
$\Rightarrow x+p=x$
$\Rightarrow p=x-x=0$
Thus, $p=0$.
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