There is no one right answer to this type of questions. The next element can be anything you want.
That is one of the typical IQ questions of the type what is the next in a sequence, by inferring it from the previous values.
The answer is, the next item can be anything you want, the book can come up with some rules to justify the next element, but so can anyone.
For example given the sequence 1,2,3,4,5,6,7,8,9, what is the next element?
It is very easy to construct a function where the next elements will be $\pi , -1 , 0$ , ( look up Lagrange Interpolation).
This is not a logic question, the book is using a wrong example regarding (mathematical) logic.
But a constructive sequence rule like $2k, k=1,2,3,4,..,n$, will let you know how to construct the elements.
Best Answer
Break up the sequence into the even ordered terms and odd ordered.