Suppose there are three items that satisfy the meaning of the question, which are respectively set as a(n- 1), an, and a(n+ 1). If a geometric series is formed, there are.

Ann? =a(n- 1)a(n+ 1)

(pn？ +xq？ )? =[p(n- 1)？ +xq？ ][p(n+ 1)？ +xq？ ]

Pack up, take it

-p(2an+p)=0

P=0 or an=-p/2

When p=0, an=xq?

That is, only when the series {an} is a constant series, all terms are equal to -p/2 (p≠0) or xq? (x, q≠0), there are three consecutive terms to form a geometric series. In other cases, they all constitute geometric series.