(Solved): In the following image, there is a sequence of three-dimensional shapes that have been created by s ...

In the following image, there is a sequence of three-dimensional shapes that have been created by stacking cubes into a corner of a room. The structure is one cube high in the first stack, two cubes high in the second stack, three cubes high in the third, and so on. Suppose the $n$th term of the sequence $P_n$ is how many cubes it would take to build the $n$th structure. Determine a recursive formula for $P_{n+1}$. Read more about 3-D patterns. $\begin{array}{l}{P}_{n+1}=P_n+4n\\ P_{n+1}=P_n+(n+1{)}^2\\ P_{n+1}=n^3?3\\ P_{n+1}=P_n+n^2\end{array}$