Question

设Sn为数列〔An〕的前n项和，已知S3等于7，A1＋3，3A2，A3＋4构成等差数列 1：求A2的

设Sn为数列〔An〕的前n项和，已知S3等于7，A1＋3，3A2，A3＋4构成等差数列
1：求A2的值
2：若｛An｝是等比数列，且An＋1＜An（n为正整数），试求Sn的表达式

Answer 1

S3 = A1+A2+A3 = 7
3A2-A1-3 = A3+4 - 3A2
6A2 = A1+A3 + 7
A1+A3 = 6A2 -7
A2 = 2

2. A2 = A1 * r so A1 = A2/r = 2/r
A3 = A2 * r so A3 = 2r
2/r + 2 + 2r = 7
2r^2 -5r + 2 = 0
(2r - 1)(r-2) = 0
r = 1/2
A1 = 4
A2 = 2
A3 = 1
Sn = (1-(1/2)^n) * 2 * 4 = 8 (1-1/2^n)