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# RD Sharma Class 10 Chapter 9 Solutions (Arithmetic Progressions)

Our RD Sharma Class 10 Maths Solutions Chapter 9 – Arithmetic Progressions cover all key areas such as the meaning of Arithmetic Progressions, nth term of an AP and sum of the first n given terms of an AP. Our RD Sharma Solutions enable you to develop an in-depth understanding of what are sequences, what is arithmetic progression, how to describe the sequence by writing the algebraic formula for given terms, how to find the sum of the given terms of an AP and how to solve various word problems related to Arithmetic Progressions.

RD Sharma Solutions for Class 10 Maths Chapter 9 answers all 77 questions asked in a total of 6 exercises. This chapter teaches you about the number of patterns observed in daily life, where successive terms are found by adding a fixed number to the preceding terms. You also learn how to calculate ‘nth’ terms and the sum of n consecutive terms. This chapter teaches you how to use this knowledge to solve some daily life problems.

Our RD Sharma Solutions contain a collection of all the tips and techniques required to solve questions from the topic Arithmetic Progressions (AP). Questions are solved in such a manner that they make the process of learning easy and highly effective. The language used for demonstration is simple and lucid. Our RD Sharma Solutions answer all questions from all exercises present in the book in a step by step manner.

## Class 10 Maths Arithmetic Progression: Important Topics

As discussed, Class 10 Maths Arithmetic Progression is one of the important chapters from the Class 10 board examination viewpoint. Here you will be learning various AP related interesting topics. Some of them have been elaborated below.

• Arithmetic Progressions

In this chapter, you will first learn that every entry in a series of numbers is known as a ‘term’. An arithmetic progression (AP) is a series of several numbers, where every term is obtained by adding a particular number to the preceding. The first term is excluded from this process. This specific number is called the common difference of the AP, which can be positive, negative or zero. An arithmetic progression can be represented in a general form as below

a, a + d, a + 2d, a + 3d, and so on.

where, the first term is ‘a’, and the common difference ‘d’.

Here you will also learn that an arithmetic progression with a fixed number of terms is known as finite AP and it contains an end term, that is the last term of A.P.The A.P. which doesn’t contain any last term is known as infinite AP.

In general, an AP can be represented as – a1, a2 … an, and d = ak + 1 – ak.

where ak + 1 and ak are the (k + 1) th and the kth terms respectively.

So, a given series of numbers a1, a2, a3 . . . is called an Arithmetic Progression, provided that the differences a2 – a1, a3 – a2, a4 – a3 … give the same value.

• nth term of an AP.

The nth term of an Arithmetic Progression is given by the general formula

an = a + (n – 1) d.

Here, the first term is ‘a’ and the common difference is’d’. Here, an is also called the general term of the AP Suppose, there are m terms in the AP, then am represents the last term which can also be denoted by the term l.

• Sum of First n Terms of an AP.

The general equation for calculating the sum of the first n terms of an AP is as follows.

S = n/2 [2a + (n-1) d]

Summation of all the terms of a given AP is given by the following equation.

S = n/2 (a + l)

Where, l is the last term (or the nth term) of the given finite AP The total of first n terms of the AP is denoted by Sn, rather than using the term S.

### RD Sharma Class 10 Maths Chapter 9: Exercise Discussion

This chapter of RD Sharma Class 10 Maths contains a total of 6 exercises and

Exercise 9.1

It contains 1 question with 9 subparts, all of which ask you to find the first term of a series where the nth term of the series is given.

Exercise 9.2

It contains 3 questions, and all of these questions test your knowledge about finding a common difference between the terms and finding the nth term of a series.

Exercise 9.3

It contains 3 questions. Question 1 has 4 subparts, all of which ask you to determine the common difference and the first term of a series. Question 2 has 3 subparts, and all of them need you to write the arithmetic progression, where the first term and common difference is given in each case. Question 3 has 3 subparts, and all of them are word problems based on concepts of arithmetic progression formation, first and last term and common difference.

Exercise 9.4

It contains 27 questions. Question 1 has 7 subparts, and Question 2 has 5 subparts, all of which ask you to determine the nth term of a series. Question 3 has 3 subparts asking you to predict if the given term belongs to the given AP Question 4 has 4 subparts, all of which ask you to determine the total number of terms in a given AP Question number 5 to 27 are all word problems based on the concept of finding nth term and the total number of terms of a series.

Exercise 9.5

It contains 6 questions, all of which are word problems in the form of linear equations where all of the questions test your knowledge about common difference, nth term determination and summation of terms of AP.

Exercise 9.6

It contains 37 questions. Question 1 has 8 subparts, followed by word problems 2 to 4 where all of which are based on the summation of terms. Question 5 has 4 subparts asking to find the sum of the first 15 terms of given series. Questions 6 to 37 are word problems based on the application of knowledge of summation of the first few terms of a series and related concepts.

### Benefits of RD Sharma Class 10 Maths Solutions for Chapter 9 – Arithmetic Progressions

• RD Sharma Class 10 Maths Solutions for Chapter 9- Arithmetic Progressions have been meticulously prepared by using the best techniques of solving AP questions.
• After practising the problems, you will effectively learn the use of arithmetic progression in your daily life problems.
• Our subject experts have drafted the solutions carefully and methodically so that you can reap the maximum benefits.
• The solution provided enables you to prepare yourself fully to attempt and answer any question from this topic in your board exams.

Our smart study tips and techniques help you remember and revise the topics of this chapter effectively and score well in Class 10 board exams and other competitive exams.

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