> What I think Ralph suggested (with tongue firmly in cheek?
Of course I did "figure out" that "a.p." meant "arithmetic progression", though that is probably by now an archaic designation for what these days are usually called "arithmetic *sequences*". Once Ms Marx (the author of that problem) limited it to being about an a.p. she was of course right in getting the value of a(88), for in the case of arithmetic sequences it takes only two terms to determine all the others uniquely.
But I pretended ignorance of the meaning of "a.p." in order to deliver my short lecture on the indeterminate nature of problems of this type, frequently found in elementary textbooks, and exams, too, where it is expected the student will *deduce* from the first few terms what the nature of the sequence must be. Well, he can guess, or read the mind of the person who set the problem, but students ought not to be subject to arguments that begin, "Well, you can tell from the differences ..." A *mathematical* question doesn't allow such observations as proofs.
Ron Ferguson quite correctly elaborated this point.
Over the years that I have seen problems of the incomplete kind (such as asking for the next term of a finite list of numbers, without fully stating the rule that makes an answer possible) I have come to the conclusion that the authors might in many cases be aware that "if you want to be fussy" there is no unique answer, but are also aware that the children giving the expected answer will have guessed what was in his mind, while the other students, less skilled at solving exam problems, are not catching on. Thus such "problems" are considered worthy in that they do what exam questions ought to do, which is to distinguish those students who have learned their lessons from those who have not.
Well, yes, but those particular "lessons" ought not to be taught.