设数列{An}是公差不为零的等差数列,Sn是数列的前n项和,且S3^2=9S2,S4=4S2,则数列{An}的通项公式是?
问题描述:
设数列{An}是公差不为零的等差数列,Sn是数列的前n项和,且S3^2=9S2,S4=4S2,则数列{An}的通项公式是?
答
(a1 + a2 + a3)^2 = 9 (a1 + a2)(a1 + a2 + a3 + a4) = 4(a1 + a2)设 公差为d, 则(a2 - d + a2 + a2 + d)^2 = 9(a2 - d + a2)(a2 -d + a2 + a2+d + a2 + 2d) = 4(a2 - d + a2)9a2^2 = 9 (2a2 - d)4a2 + 2d = 4(2a2 -...