Skip to content
Related Articles

Related Articles

Improve Article

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

  • Last Updated : 03 Sep, 2021
Geek Week

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.

Ak = Ak-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 nth term denoted by An is given by,



An = 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

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

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

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

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

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

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

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

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

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

Attention reader! All those who say programming isn’t for kids, just haven’t met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12. 

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

My Personal Notes arrow_drop_up
Recommended Articles
Page :