Q. Which is preferred, (n + 1)st or (n + 1)th?
A. An argument can be made for either, and they are both relatively common, as this extensive thread at Stack Exchange’s English Language & Usage forum suggests. If you need a source to back up one choice or the other, a user named Mitch found one: Handbook of Writing for the Mathematical Sciences, by Nicholas J. Higham (2nd ed., Society for Industrial and Applied Mathematics, 1998).
Higham’s book says that the ordinal suffix depends on the number rather than on the variable—as in (k + 1)st, (k + 2)nd, (k + 3)rd, (k + 4)th, and so on (see section 5.5, p. 63). Any variable alone would use th (kth), because k is equivalent to (k + 0), and the ordinal for zero is zeroth.
As that same Stack Exchange thread points out, some sources use a hyphen before the ordinal ending: (k + 1)-st. The thread also suggests that a preference for th treats k + 1 as a variation on kth, whereas st favors pronunciation (as in “kay plus first”).
Or see the Encyclopedia of Mathematics (European Mathematical Society, 2002), available online at https://encyclopediaofmath.org/. Usage there varies, from (n + 1)th (under “Markov braid theorem”) and (n − 1)-th (“Fredholm equation”) to (n + 1)st (“Zipf law”) and (n − 1)-st (“Weyl method”). (Other variables, including k, follow a similar pattern.) But the st variations (with or without a hyphen) seem to be more common than the ones with th, lending support to Higham’s recommendation.
Verdict? (n + 1)st, barring a strong author or publisher preference for th.