If $x + 1, 3x$ and $4x + 2$ are in A.P., find the value of $x$.

Given:

$x + 1, 3x$ and $4x + 2$ are in A.P.

To do:

We have to find the value of $x$. 

Solution:

If the given terms are in A.P., then their common difference is equal. Therefore,

$(3x)-(x+1)=(4x+2)-(3x)$

$3x-x-1=4x-3x+2$

$2x-1=x+2$

$2x-x=2+1$

$x=3$

The value of $x$ is $3$.