What is the nth term of 6 13 20 27?

The nth term is 7n-1 and so the next number will be 34

According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.
The simplest rule for the given sequence of numbers is Un = 7*n - 1 so that U6 = 41.