Update Sequence.md

Added properties and formulas related to arithmetic sequences.

Author: HowCam

docs/math/Sequence.md

@@ -47,12 +47,21 @@ $$S_n = \frac{n(a_1 + a_n)}{2} = \frac{n[2a_1 + (n-1)d]}{2}$$
 | 性质       | 内容                                                       |
 | ---------- | ---------------------------------------------------------- |
 | 对称性     | $a_1 + a_n = a_2 + a_{n-1} = \cdots$                       |
+| 下标等差    | $a_n, a_{n + k}, a_{n + 2k}, ...$ 是等差数列               |
 | 下标和     | $m + n = p + q \implies a_m + a_n = a_p + a_q$             |
 | 等距性     | $a_{n+k} - a_n = kd$（差与起点无关）                       |
 | $S_n$ 形式 | $S_n = \dfrac{d}{2}n^2 + \left(a_1 - \dfrac{d}{2}\right)n$ |
 | $S_{m+n}$  | $S_{m+n} = S_m + S_n + mnd$                                |
 | 奇数项和   | $a_1 + a_3 + \cdots + a_{2n-1} = n^2 d + a_1 n$            |
 
+**等差数列前n项和其它性质**
+
+1. $\frac {a_n} {b_m} = \frac {S_{2n-1}} {T_{2m-1}} = \frac {2m-1} {2n-1} $
+
+2. $\{ \frac {S_n} {n} \}$ 是等差数列.
+
+3. $ S_{2n} - S_{2n-1} = nd.S_{2n-1} - S_{2n-2} = a_n. $
+
 ---
 
 ### 1.3 等比数列（基础知识）
@@ -776,4 +785,4 @@ $$(1+x)^n \geq 1 + nx \quad (x > -1,\ n \in \mathbb{N}^*)$$
 
 ---
 
-*整理自：知乎、Bilibili、学科网、高考直通车、高考真题等多个来源*
+*整理自：知乎、Bilibili、学科网、高考直通车、高考真题等多个来源*