What would be the 11th number?

I am an unusually interested person in number sequences, but I don't necessarily like quizzes about them. Given a number sequence unconditionally, it is obviously possible to construct another sequence in which the first 10 terms are the same and the 11th term is different.

That said, I did come up with one quiz: What number goes in the 11th box on the right? 

One can think of it in the same way as the number in the 11th box on the left.

Header image credit:

https://www.youtube.com/watch?v=EK32jo7i5LQ

⬆️ This video is not related to the above quiz at all, but is elementary yet very educational using Archimedean Spiral (NOT Ulam Spiral). While digressing from the above quiz, but it illustrates the following:

As an approximation of pi (π), 355/113 is the second most famous after 22/7. 

Dirichlet’s theorem