Question:
Find the value of x for which the numbers (5x + 2), (4x − 1) and (x + 2) are in AP.
Solution:
It is given that (5x + 2), (4x − 1) and (x + 2) are in AP.
$\therefore(4 x-1)-(5 x+2)=(x+2)-(4 x-1)$
$\Rightarrow 4 x-1-5 x-2=x+2-4 x+1$
$\Rightarrow-x-3=-3 x+3$
$\Rightarrow 3 x-x=3+3$
$\Rightarrow 2 x=6$
$\Rightarrow x=3$
Hence, the value of x is 3.