Arithmetic Sequences - Definition & Examples

You're on the Expii Titanic and wouldn't you know, it's sinking. But you don't want to give up the ship. Since it's sinking slowly you decide to measure the water level each hour. After the first hour the boat is filled with $1\frac23$ feet of water. After the second hour the boat is filled with $4$ feet of water. After the third hour the boat is filled with $6\frac13$ feet of water.

Find an expression for the amount of water after the $n^{\text{th}}$ hour.