问题问题156已知{an}是公比为q的无穷等比数列,an∈R,|q|≠1,问是否存在这样的公比q,使等比数列{an}中有四项成等差数列?猜测1取q=52-1,则a1+a4=2a2,a1,a2,a4成等差数列,类似地,等比数列{an}中可能存在四项成等差数列.猜测2结论“在一个公比非±1的无穷等比实数列{an}中,没有无 Problem 156 It is known that {an} is a series of infinite geometric ratios with a common ratio q, an∈R, |q|≠1, and ask if there is a common ratio q such that there are four items in the {a} series of geometric progressions. The arithmetic series 1 guesses that q=52-1, then a1+a4=2a2, a1, a2, a4 are equal arithmetic series. Similarly, there may be four arithmetic series in the {an} series. 2 Conclusions: "In an infinitely proportional real number column {an} of a common ratio non-1, there is no