Question

Find the value of x for which the numbers (5x + 2), (4x − 1) and (x + 2) are in AP.

Answer 1

It is given that (5x + 2), (4x − 1) and (x + 2) are in AP.
$$\begin{gathered} \therefore \left(4x-1\right)-\left(5x+2\right)=\left(x+2\right)-\left(4x-1\right) \\ \Rightarrow 4x-1-5x-2=x+2-4x+1 \\ \Rightarrow -x-3=-3x+3 \\ \Rightarrow 3x-x=3+3 \end{gathered}$$
$$\begin{gathered} \Rightarrow 2x=6 \\ \Rightarrow x=3 \end{gathered}$$

Hence, the value of x is 3.