# Write the first four terms of the AP where a = 10 and d = 10

Arithmetic is a branch of mathematics that deals with the common operations performed in numbers which include addition, subtraction, multiplication, and division. Arithmetic is considered an elementary part of number theory; the term arithmetic was used as a synonym for number theory until the beginning of the twentieth century.

### Progression

Progression can be considered as a sequence of numbers, where each member is evaluated according to the previous member of the sequence. Generally, progression is of three basic types,

- Arithmetic progression (A sequence where the next term is ahead of the previous term by a certain real number known as common difference)
- Geometric progression (A sequence where each term except the first is evaluated by multiplying the previous term with a non-zero real number known as common ratio)
- Harmonic progression (A sequence of numbers whose reciprocal forms arithmetic progression)

### Arithmetic Progression

Arithmetic Progression is a sequence where each term except the first is evaluated by adding a certain real number to the previous term, and that real number is called a common difference.

**A _{k }= A_{k-1} + d**

Here, d is a common difference. Let’s denote the first element of the sequence as “a”, common difference as “d”, then, the element at n^{th} term denoted by A_{n} is given by,

**A _{n} = a + (n-1) × d **

### Write the first four terms of the AP where a = 10 and d = 10

**Solution:**

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

Putting n = 1

A

_{1 }= 10 + (1 – 1) × 10 = 10Hence, the first element is 10

Putting n = 2

A

_{2 }= 10 + (2 – 1) × 10 = 20Hence, the Second element is 20

Putting n = 3

A

_{3 }= 10 + (3 – 1) × 10 = 30Hence, the third element is 30

Putting n = 4

A

_{4 }= 10 + (4 – 1) × 10 = 40The fourth element is 40

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

### Similar Problems

**Question 1: Write the first four terms of the AP where a = 1 and d = 2.**

**Solution:**

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

Putting n = 1

A

_{1 }= 1 + (1 – 1) × 2 = 1Hence, the first element is 1

Putting n = 2

A

_{2 }= 1 + (2 – 1) × 2 = 3Hence, the Second element is 3

Putting n = 3

A

_{3 }= 1 + (3 – 1) × 2 = 5Hence, the third element is 30

Putting n = 4

A

_{4 }= 1 + (4 – 1) × 2 = 7Hence, the fourth element is 7

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

**Question 2: Write the first four terms of the AP where a = 2 and d = -2.**

**Solution:**

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

Putting n = 1

A

_{1 }= 2 + (1 – 1) × (-2) = 2Hence, the first element is 2

Putting n = 2

A

_{2 }= 2 + (2 – 1) × (-2) = 0Hence, the Second element is 0

Putting n = 3

A

_{3 }= 2 + (3 – 1) × (-2) = -2Hence, the third element is -2

Putting n = 4

A

_{4 }= 2 + (4 – 1) × (-2) = -4Hence, the fourth element is -4

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

**Question 3: Write the first four terms of the AP where a = 1 and d = 0.5.**

**Solution:**

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

Putting n = 1

A

_{1 }= 1 + (1 – 1) × (0.5) = 1Hence, the first element is 1

Putting n = 2

A

_{2 }= 1 + (2 – 1) × (0.5) = 1.5Hence, the Second element is 1.5

Putting n = 3

A

_{3 }= 1+ (3 – 1) × (0.5) = 2Hence, the third element is 2

Putting n = 4

A

_{4 }= 1 + (4 – 1) × (0.5) = 2.5Hence, the fourth element is 2.5

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

**Question 4: Write the first four terms of the AP where a=2 and d=10.**

**Solution:**

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

Putting n = 1

A

_{1 }= 2 + (1 – 1) × (10) = 2Hence, the first element is 2

Putting n = 2

A

_{2 }= 2 + (2 – 1) × (10) = 12Hence, the Second element is 12

Putting n = 3

A

_{3 }= 2 + (3 – 1) × (10) = 22Hence, the third element is 22

Putting n = 4

A

_{4 }= 2 + (4 – 1) × (10) = 32Hence, the fourth element is 32

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

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