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

If$(3y – 1), (3y + 5)$ and$(5y + 1)$ are three consecutive terms of an $AP$ then find the value of $y$.

Show that ${\left(a-b\right)}^2$ , $a^2+b^2$ and ${\left(a+b\right)}^2$are in $AP$.

The sum of three numbers in $AP$ is $3$ and their product is $-35$. Find the numbers.

Divide $24$ in three parts such that they are in $AP$ and their product is $440$.

The sum of three consecutive terms of an $AP$ is $21$ and the sum of the squares of these terms is $165$. Find these terms

The angles of quadrilateral are in $AP$, where common difference is ${10}^{\mathrm{o}}$. Find the angles.