# RS Aggarwal Class 11 Chapter 11 Solutions (Arithmetic Progression )

RS Aggarwal Solutions for Class 11 Chapter 11 – Arithmetic Progression is the best study resource for you as they will help you understand how to solve arithmetic progression questions in exams. This chapter includes some important concepts such as sequence, series, properties of Arithmetic Progression, the sum of n terms of an arithmetic progression and arithmetic mean. There are 6 exercises in the chapter and around 100 practice questions.

Solving 100 questions of the chapter might not be easy for a student. So, we have created RS Aggarwal Solutions for Chapter 11 for them. These solutions will help you resolve all your doubts related to the chapter. They will help you at the time revision as well. Just look for the question that you find tough, understand how to solve it correctly and practice the question as many times as you want. All the solutions are as per CBSE exam pattern so you can easily rely on them for exam preparations

## Important Topics for RS Aggarwal Solutions for Class 11 Chapter 11 – Arithmetic Progression

- A sequence is a function whose domain is a subset of natural numbers. If the range of a sequence is a subset of R (real numbers) then it is called a real sequence.
- If the sum of ‘n’ terms of a sequence is of the form An2 + Bn (A and B are constants) then, such sequence is an Arithmetic Progression or AP. The common difference of this AP is 2A.
- If a constant is added or subtracted from each term of an AP then the resulting sequence is an AP with the same common difference.
- If we multiply or divide each term of an AP a non-zero constant, then the resulting sequence will also be an AP.
- If a, b and c are 3 consecutive terms of an AP then 2b = a + c.

**Sequence**

Sequence refers to the sequence of numbers that have a difference of a constant. For eg; 5,7,9,11,… etc. This arithmetic progression has a difference of 2. Also, in the chapter, you will know about the types of sequence like real sequence and what role does it play in arithmetic progression. The difference of the constant is normally denoted by d. To find the constant difference, let us have a look at the example below:

A.P: 1,3,5,7,9,….

If you want to check that the given sequence is Arithmetic progression or not, you need to prove that the difference between the two terms should be constant.

Thus, d= a2 – a1 should be equal to a3– a2.

Here, d= 3-1=2, and 5-3=2

Thus, you can conclude that the sequence is an arithmetic progression.

**The general form of AP**

AP: a1, a2, a3, ……… an and common difference is d.

(a1 + (n – 1) d) is the general (nth) term of an AP

Sum = [(n/2) * (2a1 + (n – 1) d)] is the sum of first n terms of an AP

**Properties of an Arithmetic Progression**

**Property 1: **If you subtract or add any constant to each term of the given A.P, the resulting sequence will also be an Arithmetic Progression.

**Property 2: **If you divide or multiply each term of an A.P with a non-zero constant number, the resulting sequence will also be an A.P.

**Property 3: **In an Arithmetic Progression of the finite number of terms, the total sum of any two numbers equidistant from the beginning and the end is equal to the total sum of first as well as last term.

**Property 4: **If 2y= x+z, then the three numbers are in an Arithmetic Progression.

**Property 5: **If the nth term is a linear expression, then the sequence is an Arithmetic Progression.

**Property 6: **A sequence is an A.P. if the sum of its first n terms is of An2 + Bn, where A and B are the two constant quantities that are independent of n.

**Sum of n terms of an AP**

Sum of n terms of an AP refers to the sum of first n terms of an arithmetic sequence. Sum of n terms of an AP is equal to n divided by two times the sum of twice the first term followed by the product of the difference between third and second term, that is, ‘d’ and (n-1) is the number of terms that need to be added.

Sum of n terms of AP = n/2[2a + (n – 1)d

## Exercise Wise Discussion of Chapter 11- Arithmetic Progression

**Exercise 11A**

Exercise 11A has 31 questions in which you have to find numbers of terms of the sequence, the exact term like the 23rd term of the sequence, identify which term is let’s say 340 in AP, find common differences etc.

**Exercise 11B**

Exercise 11B has 28 questions in which you have to find some differences as asked in the question, value of x, r term of AP, the sum of n term of AP, last term of AP etc.

**Exercise 11C**

Exercise 11C has 12 questions in which you have to solve questions using the different formula of arithmetic progression.

**Exercise 11D**

Exercise 11D has 8 questions in which you have to find the arithmetic mean in different questions.

**Exercise 11E**

Exercise 11E has 6 questions in which you have to prove different situations asked in the questions.

**Exercise 11F**

Exercise 11F has 17 questions. This exercise is a mixture of all types of questions in the chapter.

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