设正项数列{an}的前n项和是sn,若{an}和{更号sn}都是等差数列,且公差相等,则a1+d=

题目

设正项数列{an}的前n项和是sn,若{an}和{更号sn}都是等差数列,且公差相等,则a1+d=
大神~求解,过程要详细点,谢谢~

答案

设公差为d,首项a1Sn=na1+n(n-1)d/2√Sn=√(S1)+(n-1)d=√(a1)+(n-1)d 平方Sn=a1+2√(a1)*(n-1)d+(n-1)^2d^2na1+n(n-1)d/2=a1+2√(a1)*(n-1)d+(n-1)^2d^2(n-1)a1+n(n-1)d/2=2√(a1)*(n-1)d+(n-1)^2d^2a1+nd/2=2√(a1)...