Write down the differences between each number and the number after it.
There is a pattern in the amounts by which the numbers increase.

The difference between $1$ and $3$ is $2$, the difference between $3$ and $7$ is $4$, the difference between $7$ and $13$ is $6$, and the difference between $13$ and $21$ is $8$. The amount added follows the pattern $2$, $4$, $6$, $8$, and so on.