写出 AP 的前四项，其中 a = 10 和 d = 10

算术是数学的一个分支，它处理以数字执行的常见运算，包括加法、减法、乘法和除法。算术被认为是数论的基本部分；算术这个词一直被用作数论的同义词，直到 20 世纪初。

进步

进展可以被认为是一个数字序列，其中每个成员都根据序列的前一个成员进行评估。一般来说，进展分为三种基本类型，

• 算术级数（下一项比上一项领先某个实数的序列，称为公差）
• 几何级数（一个序列，其中除第一项外的每个项都通过将前一项与称为共同比率的非零实数相乘来评估）
• 调和级数（倒数形成算术级数的数字序列）

算术级数

算术级数是一个序列，其中除第一项外的每个项都通过在前一项上添加某个实数来评估，并且该实数称为公差。

A _k = A _k-1 + d

这里，d 是一个共同的差异。让我们将序列的第一个元素表示为“a”，共同差表示为“d”，然后，由 A _n表示的第ⁿ项的元素由下式给出，

A _n = a + (n-1) × d

写出 AP 的前四项，其中 a = 10 和 d = 10

解决方案：

According to the problem statement a = 10 and d = 10  

Putting n = 1

A₁ = 10 + (1 – 1) × 10 = 10

Hence, the first element is 10

Putting n = 2

A₂ = 10 + (2 – 1) × 10 = 20

Hence, the Second element is 20

Putting n = 3

A₃ = 10 + (3 – 1) × 10 = 30

Hence, the third element is 30

Putting n = 4

A₄ = 10 + (4 – 1) × 10 = 40

The fourth element is 40

Hence, the first four terms of the AP are 10, 20, 30, 40

类似问题

问题 1：写出 AP 的前四项，其中 a = 1 和 d = 2。

解决方案：

According to the problem statement a=1 and d=2  

Putting n = 1

A₁ = 1 + (1 – 1) × 2 = 1

Hence, the first element is 1

Putting n = 2

A₂ = 1 + (2 – 1) × 2 = 3

Hence, the Second element is 3

Putting n = 3

A₃ = 1 + (3 – 1) × 2 = 5

Hence, the third element is 30

Putting n = 4

A₄ = 1 + (4 – 1) × 2 = 7

Hence, the fourth element is 7

Hence, the first four terms of the AP are 1, 3, 5, 7

问题 2：写出 AP 的前四项，其中 a = 2 和 d = -2。

解决方案：

According to the problem statement a = 2 and d = -2  

Putting n = 1

A₁ = 2 + (1 – 1) × (-2) = 2

Hence, the first element is 2

Putting n = 2

A₂ = 2 + (2 – 1) × (-2) = 0

Hence, the Second element is 0

Putting n = 3

A₃ = 2 + (3 – 1) × (-2) = -2

Hence, the third element is -2

Putting n = 4

A₄ = 2 + (4 – 1) × (-2) = -4

Hence, the fourth element is -4

Hence, the first four terms of the AP are 2, 0, -2, -4

问题 3：写出 AP 的前四项，其中 a = 1 和 d = 0.5。

解决方案：

According to the problem statement a = 1 and d = 0.5  

Putting n = 1

A₁ = 1 + (1 – 1) × (0.5) = 1

Hence, the first element is 1

Putting n = 2

A₂ = 1 + (2 – 1) × (0.5) = 1.5

Hence, the Second element is 1.5

Putting n = 3

A₃ = 1+ (3 – 1) × (0.5) = 2

Hence, the third element is 2

Putting n = 4

A₄ = 1 + (4 – 1) × (0.5) = 2.5

Hence, the fourth element is 2.5

Hence, the first four terms of the AP are 1, 1.5, 2, 2.5

问题 4：写出 AP 的前四项，其中 a=2 和 d=10。

解决方案：

According to the problem statement a = 2 and d = 10  

Putting n = 1

A₁ = 2 + (1 – 1) × (10) = 2

Hence, the first element is 2

Putting n = 2

A₂ = 2 + (2 – 1) × (10) = 12

Hence, the Second element is 12

Putting n = 3

A₃ = 2 + (3 – 1) × (10) = 22

Hence, the third element is 22

Putting n = 4

A₄ = 2 + (4 – 1) × (10) = 32

Hence, the fourth element is 32

Hence, the first four terms of the AP are 2, 12, 22, 32