在等差数列{an}中, a1=1,前n项的和sn满足条件S2n⼀S2=(4n+2)⼀(n+1),n=1,2....

2025-05-23 08:14:16
推荐回答(1个)
回答1:

注意等差数列的求和公式是Sn=n*(a1+an)/2=n*[a1+a1+(n-1)*d]/2=(n^2*d-n*d+2*n*a1)/2
s2n/sn=(4n+2)/(n+1)=A(4n²+2n)/A(n²+n)=[d/2*(4n²)+(a1-d/2)*(2n)]/[d/2*(n^2)+(a1-d/2)*n]

有d/2=a1-d/2=A=1
即d=2,a1=2