下面是我校高三文、理科模拟考试卷上的两道填空题:文科题设等差数列{a_n}的前n项和为S n,已知a13>0,a14<0,a13>a14,若S k S k+1<0,则k=________.理科题设等差数列{a n}的前n项和为S n,已知S13>0,S14<0,若a k a k+1<0,则k=________.两题结构对称,“个性”鲜明,精巧雅致,独具特色:其一,两题涉及了等差数列中一类“存在k∈N*使 The following are two fill-in-the-blank questions on the High School Sanctions and Science Mock Tests in our school. The first n terms and the S n of the aesthetical subjects such as a_numbers in the liberal arts are a13> 0, a14 <0, a13> a14, If k S k + 1 <0, then k = ________. The sciences set the first n terms of the arithmetic progression {an} and are S n, and S13> 0 and S14 <0 are known. If aka k + 1 <0 , Then k = ________. The structure of the two questions is symmetrical and ”personality“ is distinctive, exquisite and elegant. The first and the second questions relate to the existence of a class of ”k∈N *