题目设各项均为正整数的无穷等差数列{a_n}中,满足a_(54)=2014,且存在正整数k,使a_1,a_(54),a_k成等比数列,则公差d的所有可能取值之和为_____.答案92.分析一考虑到数列的各项均为正整数,且2014分解质因数为2014=2×19×53,所以对a_1,a_k分类讨论即可。但由于整个过程中没有考虑k为正整数,所以最后的结果需检验. The problem is to set a_ (54) = 2014 in an infinite sequence of numbers {a_n}, all of which are positive integers. If there exists a positive integer k such that a_1, a_ (54) and a_k are in an equal number sequence, The sum of all possible values ​​is _____. Answer 92. In the analysis, considering that all the items in the series are positive integers and the 2014 factor of disintegration is 2014 = 2 × 19 × 53, the discussion of a_1 and a_k can be discussed. However, since the whole process does not consider k as a positive integer, the final result needs to be tested.