SGMC Maths for 10+2

© ® Written by Sankar Ghosh Hello friends! I hope you are doing well. Over the last three blog posts, we explored Arithmetic Progression (A.P.) in depth — from its definition and general term to the sum of n terms, properties, and even special series. Each article was filled with detailed explanations, examples, and exercises to make learning easier. Now, it’s time to begin a new journey!  In today’s post, we enter into the world of Geometric Progression (G.P.). We’ll understand its basics, explore its general term, middle term and sum to `n` terms and gradually move towards problem-solving. As always, I look forward to your valuable comments and suggestions. Your feedback helps me improve and keeps me motivated to share more with you! Introduction:  Geometric Progression (G.P.) In the last three blog post, we studied Arithmetic Progression (A.P.), where the difference between two consecutive terms is always the same. For example: 1, 3, 5, 7, … → here the common difference is ...

  © ® Written by Sankar Ghosh Hello friends! I hope you are doing great. I’ve already shared two blog posts on Arithmetic Progression (A.P.), where we explored its basic concepts, general term, various types of problems, and how to find the sum of n terms and the arithmetic mean. Today, I’m bringing you the final post on Arithmetic Progression. In this post, we will discuss the important properties of A.P. and also look at some special series related to it. With this, we will wrap up our journey through A.P. and get ready to move on to an exciting new topic — Geometric Progression (G.P.) in my upcoming fourth blog post. I would love to hear your feedback and suggestions. Your support keeps me motivated to share more with you! Important properties of A.P.  (a) If a non-zero constant is (i) added to or  subtracted from each term  of an A.P. then the newly form sequence is an A.P. (b) If each term of an A.P.  is multiplied or divided by a nonzero constant  the...

  © ® Written by Sankar Ghosh Hello friends! I hope you are all doing well and staying happy. In my last blog, I discussed the concept of a sequence, what an arithmetic progression (A.P.) is, and how to find its general term. We also looked into special cases such as when 3 terms or 4 terms are in A.P., along with different types of problems related to these topics. In today’s post, I will take the discussion forward and explain how to find the sum of n terms of an A.P. as well as the concept of the arithmetic mean. I would love to hear your thoughts on the post. Please share your comments and suggestions—they will help me improve further! Sum to n terms of an A.P. Let the first term and common difference of an A.P. are `a` and `d` respectively and sum to `n` terms of the A.P. be `S_n`.  `\therefore`   `S_n=a+\left(a+d\right)+\left(a+2d\right)+...+\left(l-2d\right)+\left(l-d\right)+l`     [where `l=a+\left(n-1\right)d`] `\implies` `S_n=l+\left(l-d\right)+\l...