Generic selectors
Exact matches only
Search in title
Search in content
Post Type Selectors

Arithmetic Sequence Class 10

By Truemaths Tech,    Last Updated 14 Jun, 2023    4 min read

Arithmetic sequence: An introduction with examples

Arithmetic sequence: An introduction with examples

In mathematics, the arithmetic sequence is widely used to find the correct sequence of the given data values. Sequence means the ordered list of values in a particular pattern, like taking the common difference.

The list of numbers that have the same common difference is said to be a sequence with accurate order. There are several ways to determine the sequence of the list of numbers. In this article, we will learn all the basics of the arithmetic sequence along with solved examples.

Learn Some Amazing Maths Tricks

What is the arithmetic sequence?

A list of numbers in which the difference among two successive terms is the same or constant is said to be the arithmetic sequence. The sequence of arithmetic can be started from any number either positive or negative but the common difference between the terms must always be the same.

Integers, whole numbers, natural numbers, odd numbers, even numbers, etc. are examples of the arithmetic sequence as the difference between each successive term of these numbers is the same.

The positive difference among the sequences is said to be the increasing sequence or the positive difference for the positive integers is said to be the increasing sequence. 

For example, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53,… is an increasing arithmetic sequence as the starting term is 35 and the common difference among two successive terms is two. While a negative difference among two consecutive terms or a positive difference between two terms for the negative integer is said to be the decreasing sequence.

For example, 11, 8, 5, 2, -1, -4, -9, -10, -13, -16, -19, … is a decreasing sequence as the starting term is 11 and the difference between two successive terms is negative three.

Still finding a Maths Mentor?

Arithmetic sequence formula

The formulas for the arithmetic sequence are of three kinds such as for the nth term, the sum of series, & the common difference. 

The formula for finding the nth term of the sequence is: 

nth term = bn = b1 + (n – 1) * d

The formula for determining the sum of the sequence is:

Sum of the sequence = s = n/2 * (2b1 + (n – 1) * d)

The formula for finding the difference between two consecutive terms is: 

Common difference = d = bn – bn-1 

How to find the arithmetic sequence?

The arithmetic sequence can be determined easily by using its formulas. Let us take a few examples to solve the problems of arithmetic sequence manually. 

Example-I: For the nth term 

Calculate the 17th term of the sequence, if the arithmetic sequence is 2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, …

Solution 

Step-I: First of all, write the list of given numbers.  

2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, …

Step-II: Identify the first term, nth term, and the difference between two consecutive terms.  

nth term = 17

first term = b1 = 2

second term = b2 = 7

Common difference = d = b2 – b

                                           = 7 – 2

                                           = 5

Step-III: Take the formula of the nth term to calculate it. 

nth term of the sequence= bn = b1 + (n – 1) * d

Step-IV: Now put the common difference, first term, and the nth term of the sequence in the formula.

17th term of the sequence= b17 = b1 + (17 – 1) * d

                                                        = 2 + (17 – 1) * 5 

                                                        = 2 + (16) * 5 

                                                        = 2 + 80

                                                        = 82

Use an arithmetic sequence calculator to find the nth term of the sequence in a fraction of seconds with steps.

Example II

Calculate the 150th term of the sequence, if the arithmetic sequence is 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, …

Solution 

Step-I: First of all, write the list of given numbers.  

1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, …

Step-II: Identify the first term, nth term, and the difference between two consecutive terms.  

nth term = 150

first term = b1 = 1

second term = b2 = 8

Common difference = d = b2 – b

                                           = 8 – 1

                                           = 7

Step-III: Take the formula of the nth term to calculate it. 

nth term of the sequence= bn = b1 + (n – 1) * d

Step-IV: Now put the common difference, first term, and the nth term of the sequence in the formula.

150th term of the sequence= b150 = b1 + (150 – 1) * d

                                                            = 1 + (150 – 1) * 7

                                                            = 1 + (149) * 7

                                                            = 1 + 1043

                                                            = 1044

Example III: For sum of the arithmetic sequence

Determine the sum of the first 20 terms of the sequence, if the arithmetic sequence is 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, …

Solution 

Step-I: First of all, write the list of given numbers.  

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, …

Step-II: Identify the first term, nth term, and the difference between two consecutive terms.  

nth term = 20

first term = b1 = 3

second term = b2 = 8

Common difference = d = b2 – b

                                            = 8 – 3

                                            = 5

Step-III: Take the formula of the Sum of the sequence to calculate it.

Sum of the sequence = s = n/2 * (2b1 + (n – 1) * d)

Step-IV: Now put the common difference, first term, and the nth term of the sequence in the formula.

Sum of the sequence = s = n/2 * (2a1 + (n – 1) * d)

                                             = 20/2 * (2b1 + (20 – 1) * d)

                                             = 20/2 * (2(3) + (20 – 1) * 5)

                                             = 20/2 * (2(3) + (19) * 5)

                                             = 20/2 * (6 + (19) * 5)

                                             = 20/2 * (6 + 95)

                                             = 20/2 * 101

                                             = 10 * 101

                                             = 111

You should also solve questions to get an idea of the type of questions that were asked previously.

What are some Important Maths Exam Questions?

Summary 

Now, after reading the above post, you can easily find the nth term and the sum of squares by using formulas. In this article, we have learned all the basics of the arithmetic sequence, along with examples. We also offer mathematics ncert class 10 pdf for students to practice upon. You can check our other articles to grab pdf of ncert maths class 10.

SHARE:

    Parents Reviews

    Student Reviews

    In the beginning, when I came across The Doon School Entrance Exam coaching, I was not very sure about it. Later, when I read the testimonials and contacted these people in person. Then, I got the required trust. I started the classes with a firm belief and see, now I have cleared the exam. Thank you so much.

    doon school result

    Aayansh Pandey

    Doon School

    The day I was sitting in the examination hall and took the paper in my hand, I was surprised. Most of the questions, I have already studied while my preparation. Thanks to the Experts who with their sheer hard work have made my journey so smooth.

    Doon school result

    Hridit Rohit Surana

    Doon School

    It was my immense luck and fortune to get the coaching from Truemaths for the preparation of Welham Girls'. All the teachers leave no stone unturned to shape my future.

    Welham girls result

    Tamanna

    Welham Girls' School

    Huge respect, love, and devotion to entire teachers, mentors, and experts for their blessings and hard work towards me. It's their efforts that make me to count myself into better professionals.

    the doon school result by truemaths

    Madhav Ramesh

    The Doon School

    Truemaths has been a great contributor to the development of my personality. I have established my leadership, time management, and team skills and to get the Final selection in The Doon School.

    Sahil Truemaths

    Sahil Patil

    St. George's School


    Newsletter

    STAY INFORMED & INSPIRED

    Subscribe to our Newsletter

    Got some doubts or queries?

    Schedule a one-on-one session with our Experts.

    Join WhatsApp Community