Let's take a look at what happens for every iteration, so we can identify a common pattern that allows us to write down a formula for the n-th iteration.
Let P be the number of people receiving the email.
First iteration (n=1)
Joey sent an email to 2 friends
Second iteration (n=2)
Those two friends then send it to 3 friends each:
Third iteration (n=3)
Those friends then send it to 3 friends each:
Fourth iteration (n=4)
Those friends then send it to 3 friends each:
Now the pattern becomes clear. For every iteration, we have a 2 multiplying a 3 that has a power equal to the number of the iteration minus one. This way,
n-th iteration:
In terms of the table,