Question

已知數(shù)列{a_n}是首項(xiàng)為4，公差d≠0的等差數(shù)列，記前n項(xiàng)和為S_n，若S₃和S₄的等比中項(xiàng)為S₅.

(1)求{a_n}的通項(xiàng)a_n；

(2)求使S_n＞0的最大值n.

Answer 1

解：(1)設(shè)a_n=4+(n-1)d(d≠0),S_n=4n+.

∴S₃=12+3d,S₄=16+6d,S₅=20+10d,由題設(shè)(S₅)²=(S₃)·(S₄),

即(4+2d)²=(4+d)(4+d),得d=,

∴a_n=.                                                          

(2)S_n=4n+n，∵S_n＞0,

∴＞0,得0＜n＜,又∵n∈N^*,∴n=4為所求.