Major edit: while I still personally like (k+1)th, @Mitch has found confirmation for (k+1)st in a math handbook, to which I must concur. Therefore, (k+1)st appears to be the most correct to mathematicians. Barring any future pertinent revelations, I would suggest using (k+1)st.
Kay plus first seems worse to me because one visualizes k + 1st instead of (k+1)th. If only for this reason, I would say "(k+1)th". Adding "orthographic consistency" to the mix pretty much decides the issue for me.
I would say that the only reason why it might not sound natural is because we don't say "(k+1)th" in ordinary life, hence oneth is not a usual word. However, we often use the word first, and therefore it sounds more natural. This does not mean it is the best choice.
As to which is used more often, doing the googling ("(k+1)st" -grade -grades and "(k+1)th") turns up evidence for the inference that each is used about as much as the other. (Wikipedia uses (k+1)th, however, for what it's worth, while our friends at Math.SE seem mainly to support (k+1)st.)
As for spoken usage, any would be acceptable, but all are clunky. Try to avoid such terms.
As for usage difference based on context - there does not seem to be a usage/meaning difference between the two.
Either way, spoken or written, I recommend strongly that you reword your sentence so that facing the issue is unnecessary if possible.
In Standard English, this usage of the word times is considered an error. It is often used by children and students when speaking of multiplication, for exactly the reason that you indicate: the formula X times Y equals Z has spawned the creation of a verb to times meaning to multiply.
However, using this in any kind of formal context is considered an error, and I have only ever encountered this usage from children. I would avoid it in writing altogether, and discourage students from using it.
Best Answer
I remember this usage from when I was in primary school, and I never adopted it. There are speakers, like me, for whom plus, minus and times are, in mathematics (the topic of my undergraduate degree), only the names of the operations
+,-, andx. The corresponding verbs are add, subtract, and multiply.For example, I’d say:
That said, if enough (influential) people start using plus, minus and times as verbs, then, as with every other language change, that will eventually come to be regarded as standard and, hence, correct. After all, if you can hammer with a hammer, and plough with a plough, why shouldn’t you be able to plus with a plus?