RS Aggarwal Class 11 Solutions Chapter-11 Arithmetic Progression

Progression is a term used to describe a succession whose terms follow particular patterns. Arithmetic Progression in RS Aggarwal Solutions Class 11 Maths Chapter 11 is an important chapter. It is a sequence of numbers in which the preceding term adds a constant quantity to form the consequent term. It states that the difference between the preceding term and the consequent term is a constant quantity. For example, in all the natural numbers: 1,2,3,4,5,6...the difference between two successive numbers is always 1. Also, in odd or even numbers we observe a similar thing is happening, where the difference between the two numbers always remains as 2. 

bn+1- bn = constant (=d) for all n∈ N Arithmeticc progression is about a sequence of numbers in which the difference between two terms remains constant. 

The sequence {5, 10, 15, 20, 25, 30, …………………} is an Arithmetic Progression where the common difference is 5, since

Why is it Beneficial to Learn Arithmetic Progression?

An arithmetic progression is a sequence of terms with a common difference between them that is a constant value. It's a term that's used to generalize a group of patterns that we see in our daily lives.

The capacity to notice and generate patterns aids us in making predictions based on our observations is a crucial mathematical talent. Pattern recognition helps children’s acquisition and understanding of complex numerical concepts and mathematical processes. Patterns let us recognize connections and make generalizations.

What are the Properties of Arithmetic Progression Class 11 RS Aggarwal?

The properties of arithmetic progression discussed in RS Aggarwal class 11 maths chapter 11 solutions are as follows:

Property 1: When you add or subtract any constant term to the given AP in each number, the resulting sequence will be an arithmetic progression. 

Property 2: When you multiply or divide each term of a given AP with a non-zero constant, the result will also create an arithmetic progression. 

Property 3: In a finite term of numbers of an arithmetic progression, the total summation of two numbers equidistant from the end and starting will be the numbers is the same as the total summation of the last term and first term. 

Property 4: If 2b = a+c then the three numbers are said to be in an arithmetic progression.

Property 5: A sequence will be established as an arithmetic progression if the nth term is a linear expression. 

Property 6: A sequence will be an arithmetic progression if the summation of the 1st n terms is of An2 + Bn, where A and B are said to be two constant quantities independent of n. 

Note: The effect of adding or subtracting a constant from each term of an AR is an AP with the same common difference. The resulting sequence is also an AP if each term of an AP is multiplied or divided by a non-zero constant.

What are the Benefits of  Preparing from RS Aggarwal Class 11 Maths Arithmetic Progression Exercise?

There are several benefits of preparing from RS Aggarwal Arithmetic Progression exercises. 

• Exercise 1- The first exercise contains questions, where one needs to find the number of terms in the sequence. Suppose the exact term like the 23rd term of the sequence, identifying the terms and finding the differences, etc. This exercise is a starter exercise that doesn’t include a lot of difficult questions. This exercise exists to make students used to the process of identifying the terms and finding the differences.

• Exercise 2- The second exercise has questions related to finding some differences as asked in the questions, r term of AP, the value of x, the sum of n terms of AP, last term of Ap, etc. The second exercise is one step up. The exercises in the RS Aggarwal reference book build up the difficulty level with every question you solve, ensuring that one is prepared for any kind of question that might come in the exam.

• Exercise 3- In this exercise, some questions need to be solved using the various formulas of an arithmetic progression. This is a comparatively basic exercise. Helps in making the basics strong. 

• Exercise 4- Here, students will find different questions, where one has to find the arithmetic mean. The questions in this exercise will help you brush up on your concepts.

• Exercise 5- Here students have to prove different situations that are asked in the questions. This exercise requires a good presence of mind and decent application skills. It will require you to apply the concepts that you’ve already learned and practiced differently.

• Exercise 6- The final exercise comprises various questions that are present in the overall chapter. Solving this exercise will help you assess where you stand on your overall preparation for this chapter. 

Solved Exercise Question from Arithmetic Progression

Question Given that: the nth term of series = (5a+2) 

Sol: Putting a= 1,3,5,7 in the nth term, we obtain, 

First-term a1 = (5 x 1 + 2) = 7

Second term a2 = (5 x 3 + 2) = 17

Third term a3 = (5 x 5 + 2) = 27

Fourth term a4 = (5 x 7 + 2) = 37

Therefore, the first four terms of the series are (7, 17, 27, 37)

Did You Know? 

The behaviour of an arithmetic progression depends upon the common difference. If the difference is positive, it progresses towards positive infinity, if negative it goes towards negative infinity.  The distinction between arithmetic and a geometric sequence is that the difference between two consecutive terms in an arithmetic sequence remains constant, whereas the ratio between two consecutive terms in a geometric series remains constant.

Conclusion

The chapter covers all the important questions along with the answers that serve as a ready reference to comprehend and solve various questions for examination. Students can now include it in their daily practice schedule and home task to grasp the chapter very well. RS Aggarwal Class 11 Maths Arithmetic Progression PDF by Vedantu is made according to the latest question pattern that follows in the examination. So, it will be a good resource for scoring higher marks.