CBSE Chapter Arithmetic Progression Class 10 Notes are prepared by experts that help you prepare effectively for the exam. Our notes are based on NCERT guidelines.CBSE Chapter Arithmetic Progression Class 10 Notes are well-written to help students comprehend the ideas, subjects, and issues covered in every chapter. Notes are prepared per the most recent curriculum approved by the CBSE and provide the foundation for Revision Notes. These helpful notes relieve students of the burden of purchasing several books to study for the exam time. The major benefit is that it emphasises key concepts and provides examples to explain them, motivating students to perform well on exams. Get all of the notes for arithmetic progressions in class 10. These notes are helpful for students studying for the CBSE board examinations in 2022–2023.
Below, we’ve included a summary of the CBSE Notes for Class 10, covering each concept thoroughly.
An Overview of Arithmetic Progression Class 10 Notes
- A set of integers that are created by adding a predetermined number to each term before it, beginning with the first term, while maintaining a constant distance between each succeeding word is called AP.
- The fixed value is known as the common difference of the AP and can be any integer. Each of the numbers in the list is referred to as a term. For instance: 3,8,13… with a shared difference of 5.
- For the purpose of helping learners review the whole course, arithmetic progression notes have been developed. Teachers with extensive experience in the subject have prepared the CBSE Solutions and other study materials on Arithmetic Progression. The 10th arithmetic progression Notes will enable pupils to complete their homework quickly.
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- The Class 10 arithmetic progression chapters include numerous information that students can only comprehend. The idea of a progression series is presented in the chapter on arithmetic progression (AP).
- Since this is one of the most crucial chapters in the class 10 math curriculum, mastering its complexities is necessary if you want to do well on the board test. Once you have a solid grasp of the arithmetic progression topic, you can tackle the challenging problems that are a part of competitive examinations with ease.
A series of integers that differ from one another by a common factor is known as an arithmetic progression. The sequence 2, 4, 6, 8, etc., is an A.P. with a common difference of 2. The words in the sequence are also in A.P. with the same common difference if the same number is added to or removed from each A.P. term.
- The introduction to Arithmetic Progression (AP), general terminologies, and numerous AP formulae, such as the sum of n terms of an AP, nth term of an AP, and so on, will all be covered in detail in this article.
- A sequence of numbers called an arithmetic progression is produced by starting with the first term and adding a certain amount to the term before it while keeping a fixed distance between each following term. The fixed number sometimes referred to as the AP’s common difference can be any integer. There are terms for each of the list’s numbers. As in 4, 10, 16, 22, etc., which all have a difference of 6 in common.
- Sequence: A sequence is a grouping of numbers in a certain order and in accordance with some norm. For example, the series 12,15,18,21… is one where each subsequent item is 2 bigger than the term before it, while the sequence 1, 4, 9, 16, 25,… is one where each term is the square of subsequent natural numbers.
- Series: The total of the items in the matching sequence makes up a series. An example of a natural number series is 1, 2, 3, 4, 5. A phrase is used to describe each number in a series or sequence.
- Progression: A progression is a sequence of events for which a mathematical formula may be used to represent the general term.
- Arithmetic Progression (AP): A progression in which the difference between two subsequent words is constant is known as an arithmetic progression (AP). The first term in an arithmetic progression is denoted by the letter “a,” the last term by the letter “l,” the common difference between two terms is denoted by the letter “d,” and the total number of terms is denoted by the letter “n.”
- For example, the infinite mathematical progression is 4, 10, 16, 22, and 28. Now, think about it. Here, a = 4 for the first term. The common difference is 6.
The common difference, in this case, is determined as follows:
First term – the second term is 10 – 4 = 6.
Second term – third term equals (16 – 10) = 6.
Fifth term minus fourth term equals (28 – 22) = 6.
The above progression is an arithmetic progression since the difference between two successive terms is constant, that is 6.
- Common Difference: The common difference is the distinction between an A.P.’s two consecutive terms. For instance, the common difference in the series 6, 12, 18, 24, etc., is 6. The common difference is categorised as follows
(i)positive whenever the A.P. rises.
(ii)When the A.P. is constant, it is zero.
(iii)when the A.P. is declining, negative.
The following is the formula to determine the common difference between the two terms:
common difference(d) = (an – an-1).
The term “an” denotes the nth phrase in a series. And (an-1) stands for the prior period. that is, the (n-1)th term in a series.
- General Form of an Arithmetic Progression: The words a1, a2, a3,…an are in A.P., you say. where the common difference between the first and second terms is “d.” The terms can then also be stated as shown below.
Term 1: a1 = a
Term 2: a2 = a d
Term 3: a3=A 2d
So, another way to describe arithmetic progressions is as follows: a, a d, a 2d, ……The general form of an arithmetic progression is what is known as this representation.
- Finite Arithmetic Progression: Finite Arithmetic Progression is the name given to a sequence of terms that contains a finite number of terms. For example, 229, 329, 429, 529, 629
- Infinite Arithmetic Progression: The term “infinite arithmetic progression” refers to a series that has an unlimited number of terms. For Example 2, 4, 6, 8, 10, …..
- Sum of Terms in an Arithmetic Progressions(AP): The equation for an AP’s sum to n terms. An A.P’s nth-term sum is calculated as follows:
Sn = n/2 (2a (n – 1) d)
The letter “a” stands for the first term, “d” for the common difference, and “n” for the number of terms. A is the initial term, L is the A.P.’s last term, and n is the total number of terms.
- Calculating the sum of n terms in an AP: An = a+(n – 1)d will be the nth term of an arithmetic progression if an is the nth term, a1 is the first term, n is the number of terms in the sequence, and d is a common difference.
- Example: Find the AP’s 11th term: 24, 20, 16,…
Solution: A = 24, n = 11, and d = 20 – 24 = – 4 are given.
an = a+(n – 1)d
a11 = 24+(11-1) – 4
= 24+(10) – 4
=24 – 40
- Arithmetic Mean (A.M): The simple average of a given collection of integers is known as the arithmetic mean. A group of integers’ arithmetic mean is determined by:
A.M. = Sum of terms / Number of terms.
Any set of numbers can have a specified arithmetic mean. The figures don’t have to be in an A.P. For example, if the numbers a, b, and c are in arithmetic progression, then we may say that b is the arithmetic mean of a and c since b = (a+c)/2.
- First n natural number’s sum: The sum of the first n natural numbers is calculated as follows:
This formula is created by treating the natural number sequence as an A.P., where the initial term (a) and common difference (d) are both equal to 1.
- Calculating the first n natural number’s sum:
For example, the following formula may be used to get the sum of the first 20 natural numbers:
Here, n = 20
Replace the value in the formula now by:
Sn = n(n+1)/2
S20 = [20(20+1)]/2
S20 = 420/2
S20 = 210
- The following table includes all the formulae for Arithmetic Progression class 10:
First term = a
Common difference = d
General form of Arithmetic Progression = a, a d, a 2d, a 3d,….
nth term (an) = a+(n – 1)d
Sum of first n terms (Sn) = (n/2)*[2a (n – 1)d]
Properties of Arithmetic Progressions
- The words in the sequence are also in A.P. with the same common difference if the same number is added to or removed from each A.P. term.
- The resultant series is also in A.P. if each term in A.P. is divided or multiplied by the same non-zero value.
- If 2b = ac, then three numbers, a, b, and c, will constitute an A.P.
- If the nth term in a series is a linear expression, the series is an A.P.
- If we choose terms from the A.P. at the prescribed intervals, the chosen terms will also constitute the A.P.
- The resultant sequence will also be an arithmetic progression if the terms of one are raised or lowered by the same amount.
Practice Questions as per CBSE Curriculum
Q1) Which term of the AP 3,8,13…. IS 78?
Q2) Find the sum: 34, 32, 30, . . . 10
Q3) How many terms of the AP: 9, 17, 25, . . . must be taken in order to get to the number 636?
Q4) Check whether – 150 is a term of the AP: 11, 8, 5, 2 . . .
Q5) Students in one school proposed planting trees in and around the school to minimise air pollution. It was determined that the number of trees planted by each section of each class would be the same as the number of trees planted by the class in which they are studying; for example, a section of Class I will plant one tree, a section of Class II will plant two trees, and so on until Class XII. Each class is divided into three portions. How many trees will the students plant?
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