Is there a word to describe something that is not the first element in a sequence, but can be in any other position? A synonym of "not first", in fact.
This element is __ in this sequence.
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The word has been used in literature on English grammar and other fields. Google books records, for instance:
"On the one hand, the finite verbal category seeks a noninitial position ..." -Géraldine Legendre, Jane Grimshaw, Sten Vikner: Optimality-Theoretic Syntax, 2001, p264.
"Noninitial stress may be found on any syllable of the word, and may or may not co-occur with initial stress." -Jean Ormsbee Charney: A grammar of Comanche, 1993, p41.
"Consequently, even for monosyllable words, CS and LEC factors can be distributed over different word positions in several ways: CS can be word initial (e.g., “quick”) or noninitial ..." -Peter Howell, Recovery from Stuttering, 1947, p155.
Wiktionary defines noninitial as Not initial.
"This element is __ in this sequence."
While not a single word, surely this is the most logical alternative:
"This element is "after the first element" in this sequence."
I think subsequent would be grammatically correct, albeit somewhat of an awkward sounding sentence.
"This element is subsequent in this sequence."
In the programming language Lisp, the term "head" and "tail" are used to refer to "the first item" and "everything but the first". Alternative form that are also used: "first" and "rest".
The element is the head of this sequence. The element is in the tail of this sequence.
The element is first in this sequence. The element is in the rest of the sequence.
The word sequelae at first looks promising due to its etymology: from Latin sequela, from sequi ("follow"). However, it is specialized to a medical sense, “diseases or conditions which are caused by an earlier disease or problem”. OED also shows a rarely-used sense, “A person's followers”, that is a little more general. The noun follower itself, meaning “Something that comes after another thing”, is a better possibility, along with previously-mentioned adjective following (“Coming next, either in sequence or in time”).
Subsequent (“Following in time; coming or being after something else...”) was mentioned in passing in another answer. Aside from follower, it may be the best choice among common words. Also consider succedent (“That succeeds; succeeding, following”) and successor (“a person or thing that succeeds another”).
could be used to describe any element in a list except the first, much like subsequent, and with more or less the same limitations. Both are slightly awkward as they don't have just that single exclusive meaning, but I think these two are probably the best fit out of the available options, without any further context being given.
For the more pedantic people out there, I suppose nth(n>1) would cover it, but whether this counts a single word is dubious at best. As a more compact option, I would propose defining
as having the desired meaning. This has the added benefit of easily extending to concepts like items beyond the (n>1)th in a list.