等差级数，等差数列；[数] 算术级数，算术数列
Combined with a progression arithmetic, time series analysis of rock pressure in a tunnel i.
结合累进算法，对浙江某新建隧道围岩压力进行时间序列预测。
The result shows that the utility of the arithmetic progression can limit the first kind of misread.
结果表明， 等差数列的利用可规范第一种误读。
Combined with a progression arithmetic, time series analysis of rock pressure in a tunnel in Zhejiang Province is carried out.
结合累进算法，对浙江某新建隧道围岩压力进行时间序列预测。
Arithmetic progression: a number of its change in the process, after each change in the amount of change several times before, that is the product of the relationship.
算术级数：一个数量在其变化的过程中，每一次变化后的量是变化前的若干倍，也就是乘积的关系。
What is the arithmetic progression?
什么是算术级数？
Prove that no four consecutive binomial coefficients can be in arithmetic progression .
证明不存在四个连续的二项系数成算术级数。
It is questioned that thickness curves of concrete structures having uneven surface are directly derived without migrate, and depth is taken directly from ordinate in arithmetic progression.
常见的不作偏移，即对其背后岩石凹凸不平的混凝土结构物作厚度曲线，或在时间剖面上用等差级数的深度纵坐标，有基本概念的问题。
Some special patterns of annuity changes whose payments are of the arithmetic progression of higher order or of the reverse rainbow are stu***d, and their beginning values and ending values are given.
并研究了付款额呈高阶等差数列及倒虹式年金等某些特殊的年金变化形式，给出了其期初值和期末值。
A core property of the arithmetic progression is the same difference.
高度披露在算术级数的数字，是在屏幕上闪过，一个接一个。
The formula of finite summation of K Steps arithmetic progression is seeked out by using the summation function of power series.
用幂级数和函数的思想来给出阶等差数列求有限和的公式。
By reducing positions when they were losing money, the Turtles countered the arithmetic progression toward ruin effectively.
亏损时减仓，海龟们计算连续亏损的过程。
If combined with 4 to form a tolerance of 1 arithmetic progression, option C with 4 lines out of the box area was chosen C …
如果再加上4就构成了一个公差为1的等差数列，选项C有4个出方框范围的线条，故选C…
|arithmetic series;等差级数，等差数列；[数]算术级数，算术数列
等差数列（Arithmetic Progression） 是数学中一种基础且重要的数列类型，指从第二项起，每一项与它的前一项的差等于同一个常数（称为“公差”）的数列。这个特性使得等差数列具有清晰的结构和规律性。
核心特征与公式：
公差（Common Difference, d）：这是等差数列最核心的特征，即任意相邻两项之间的差是固定不变的。公差可以是正数、负数或零。
首项（First Term, $a_1$）：数列的第一项。
通项公式（General Term Formula）：等差数列的第 $n$ 项（$a_n$）可以用首项和公差表示： $$a_n = a_1 + (n - 1)d$$ 这个公式允许直接计算数列中任意位置的项。例如，若首项 $a_1 = 5$，公差 $d = 3$，则第 4 项 $a_4 = 5 + (4-1) times 3 = 14$。
求和公式（Sum Formula）：前 $n$ 项的和（$S_n$）有两种常用形式： $$S_n = frac{n}{2} times (a_1 + a_n)$$ $$S_n = frac{n}{2} times [2a_1 + (n - 1)d]$$ 第一个公式需要知道首项和末项，第二个公式只需要首项和公差。例如，求首项为 2，公差为 3 的等差数列前 5 项的和：$S_5 = frac{5}{2} times [2 times 2 + (5-1) times 3] = frac{5}{2} times (4 + 12) = frac{5}{2} times 16 = 40$。
实际应用举例：
权威参考来源：
“Arithmetic progression”（简称AP）是数学中常见的术语，中文译为等差数列，指一个数列中相邻两项的差始终保持恒定。以下是详细解释：
通项公式：第$n$项的值$a_n$可表示为
$$
a_n = a_1 + (n-1)d
$$
其中$a_1$是首项，$n$为项数。
前$n$项和：等差数列前$n$项的和$S_n$有两种计算方式：
$$
S_n = frac{n}{2} [2a_1 + (n-1)d]
$$
或
$$
S_n = frac{n(a_1 + a_n)}{2}
$$
通过上述公式和示例，可以快速确定等差数列的任意项或总和。若需具体问题计算，可提供数值进一步演示。
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