JEE Advanced Arithmetic and Geometric Progressions Important Questions

The Arithmetic and Geometric Progressions chapters have a lot of application in numerous chapters in Math. Therefore you are advised to have numerous revisions until the fundamental concepts are completely clear to you. As math is a very important part of JEE Advanced Exams it is important not to miss these chapters as they are relatively simple and easy to score. 

Math is a chapter that needs a completely analytical and logical approach. This is the basic acumen needed for excelling in the competition. While solving Math problems, the only way to be calm and confident is through repeated practice. By practicing various types of math problems you prepare yourself to be able to solve all kinds of different questions that might or might not be asked. 

Following are the important topics in this chapter that will help you to excel in this chapter:

• Sequence

• Infinite Sequence

• Geometric progression

• General term of G.P

• Geometric Mean

• Harmonic Sequence or Progression and

• General term of H.P

• Series

• Arithmetic Sequence or Progression

• General term of A.P

• Arithmetic Mean

Arithmetic progression is where the difference between a term and its previous term is the same for the entire series. For example, if the sequence of the numbers is 2,4,6.8,... the difference between two consecutive numbers in the series is 2. Hence, we can say that the series is in arithmetic progression. In a progression, the common difference is denoted by ‘d’. The nth term is denoted by ‘an’.

Important Formulas Related to Arithmetic Progression:

The sum of the nth term is denoted by ’Sn’. A formula to define the nth term of an arithmetic progression is \[a^{n} = a + (n - 1) \times d\]. The Sum of n terms is calculated using  \[ S = \frac{n}{2} (2a + (n - 1) \times d)\]. The Sum of an arithmetic progression when the last term of the progression is known is \[S = \frac{n}{2} (first term + last term)\]. a= first term in the series, n= number of terms, and d= common difference in the series.

On the other hand, a series is said to be in geometric progression if the difference between two consecutive numbers in the series is the product of the previous number with a constant value. For example, 3,6,12,24…...in this series, the common ratio between two consecutive numbers is 2. The general form of a geometric progression is a \[ a, ar^{2}, ar^{3}, ... ar^{n}\]. Here, a denotes the first term, r is the common ratio and arn is the nth term. \[a^{n} = ar^{n-1}\] is the formula to find the nth term of a geometric progression. The Sum of n terms of a geometric progression is calculated using \[S^{n} = a + ar + ar^{2} + ar^{3} + ... + ar^{n-1}\].