已知数列{an}满足an+1+an=4n-31若数列an是等差数列,求a1的值2当a1=1时,求数列an的前n项和Sn

Question

已知数列{an}满足an+1+an=4n-3
1 若数列an是等差数列,求a1的值
2 当a1=1时,求数列an的前n项和Sn

Answer 1

若数列an是等差数列可设a(n+1)=a1+ndan=a1+(n-1)da(n+1)+an=2a1+(2n-1)d=4n-3整理,得2dn+2a1-d=4n-32d=42a1-d=-3解得d=2 a1=-1/2a1=-1/22、因为a(n+1) + an = 4n -3即a(n+1) - 2(n+1) + 5/2 = - ( an - 2n + 5/2 )令...