SGMC Maths for 10+2

  SETS   Lesson 1 In this lesson, we will discuss sets and different types of sets. First, let us understand what a set is. A set is a well-defined collection of distinct objects or elements. For example: (i) When we refer to living beings (such as human beings, animals, plants) or non-living things (such as numbers, letters, symbols, etc.), we are essentially referring to some collection. (ii) To call a collection “well-defined,” it must be clear whether a particular object belongs to that collection or not. For example: The collection of all natural numbers less than `10` is well-defined, because it is clear that `8` belongs to the collection, whereas `12` does not. The collection of all students of a particular school is well-defined, because it is clear who is a student and who is not. The collection of all capital cities in India of different states is well-defined, because each city is either a capital or not. However, if we consider the collection “the set of all bea...

© ® Written by Sankar Ghosh Hello Readers, In my previous blog post (Part 5) , I discussed the sum of n terms of a Geometric Progression (G.P.) in detail. Now, in Part 6 , we will move further and explore three important topics: 1️⃣ Properties of G.P. 2️⃣ Geometric Mean 3️⃣ Infinite Geometric Series As always, the post includes both theoretical explanations and problem-solving and concludes with an exercise section to help you strengthen your understanding. I encourage all readers to attempt the exercises for deeper learning. And of course, feel free to share your doubts in the comment section —I’ll be happy to help you clarify them. Happy Learning! Properties of Geometric Progression Let us discuss some properties of Geometric Progression (1) Square of any term (except first term and last term) is the product of its two adjacent terms. Suppose `t_1,t_2,t_3,...` etc are in G.P. Then `t_2^2=t_1t_3,t_3^2=t_2t_4,t_4^2=t_3t_5,....` etc. (2)  Square of any term (except first te...

© ® Written by Sankar Ghosh   Dear Friends, In my blog series “Progressions – A.P. and G.P.”, the first three parts were dedicated to Arithmetic Progression (A.P.), where I explained the concepts in detail along with examples and exercises. In Part 4, we moved into Geometric Progression (G.P.), focusing on the general term and solving related problems. I encourage you to try the exercises given at the end of each part—your learning will be complete only when you practice them thoroughly. And of course, if you face any difficulty or have doubts, please feel free to write in the comments. I will be more than happy to help you out. Now, in today’s post, we take the next step in our journey with G.P. — discussing the sum to n terms of a Geometric Progression. Happy learning and keep sharing your thoughts and questions with me! Warm regards, Sankar Ghosh Sum of the first `n` terms of a G.P. Let the first term of a geometric progression be `a`, common ratio `r\left(\ne1\right)` and sum o...