Class 10th L-2 MATHEMATICS || CH-5 ARITHMATIC PROGRESSIONS || NCERT ||#cbse 2025-26

Class 10th MATHEMATICS || CH-5 ARITHMATIC PROGRESSIONS || NCERT ||#cbse 2025-26 pdf of Vedio https://air.ifpshare.com/documentPrev... 📚 *Arithmetic Progressions (AP) – All Important Formulas* --- 1. *Definition of AP* A sequence is an AP if the difference between any two consecutive terms is constant. This difference is called the *common difference* \( d \). --- 2. *Common Difference (d)* Formula: \[ d = a_2 - a_1 = a_3 - a_2 = a_4 - a_3 = \text{constant} \] --- 3. *General (nth) Term of an AP* Formula for the \( n \)th term \( a_n \): \[ a_n = a + (n-1)d \] where: \( a \) = first term, \( d \) = common difference, \( n \) = number of terms, \( a_n \) = \( n \)th term. --- 4. *Sum of First n Terms (Sₙ)* Formula 1: \[ S_n = \frac{n}{2} [2a + (n-1)d] \] Formula 2 (if last term \( l \) is given): \[ S_n = \frac{n}{2}(a + l) \] where: \( l = a_n = \) last term. --- 5. *Finding Number of Terms (n)* If first term \( a \), last term \( l \), and common difference \( d \) are known: \[ l = a + (n-1)d \] Solve for \( n \) using this formula. --- 6. *Finding First Term (a)* If \( d \), \( n \), and \( a_n \) are given: \[ a = a_n - (n-1)d \] --- 7. *Finding Common Difference (d)* If two terms \( a_n \) and \( a_m \) are given: \[ d = \frac{a_n - a_m}{n - m} \] --- 8. *Special Cases* **Sum of AP where first and last term are given**: \[ S_n = \frac{n}{2}(a + l) \] **Last Term (l) formula**: \[ l = a + (n-1)d \] --- ✅ *Quick Summary Box* | Concept | Formula | |------------------------|--------------------------------------| | Common Difference | \( d = a_{n} - a_{n-1} \) | | nth Term | \( a_n = a + (n-1)d \) | | Sum of n Terms (1) | \( S_n = \frac{n}{2}[2a + (n-1)d] \) | | Sum of n Terms (2) | \( S_n = \frac{n}{2}(a + l) \) | | Finding last term (l) | \( l = a + (n-1)d \) | --- class 10 maths 2025-26 class 10 maths full syllabus 2025 class 10 maths ncert solutions 2025 class 10 maths important questions 2025 how to score 100 in class 10 maths cbse class 10 maths paper 2025 class 10 maths revision 2025-26 cbse maths 2025 class 10 class 10 maths most important questions class 10 board exam preparation maths class 10 term 1 maths 2025 class 10 term 2 maths 2025 maths sample paper 2025 class 10 class 10 maths question paper 2025 with solution ncert class 10 maths explanation 2025 best channel for class 10 maths 2025 cbse class 10 maths blueprint 2025 class 10 maths strategy 2025 class 10 maths paper pattern 2025 Class 10 Maths 2025-26 full syllabus Class 10 Maths important questions CBSE Class 10 Board Maths preparation Maths Chapter wise explanation Class 10 Class 10 Maths Sample Paper 2025 Class 10 Maths Tips and Tricks How to score 95+ in Class 10 Maths Class 10 Maths new syllabus 2025 CBSE Class 10 Mathematics solved paper Class 10 Board Exam Maths Strategy #class10maths #class10maths2025 #maths2025 #class10mathsnewsyllabus #ncertclass10maths #cbsemaths2025 #class10mathsimportantquestions #class10mathsrevision #class10boardexam2025 #cbse2025 #cbseclass10maths #mathsbychapter #class10mathsexam #maths2025board #class10termexam #10thboardexam2025 #class10cbsemaths #mathsquestionpaper2025 #mathspreviousyear #mathsmostimportantquestions #class10mathematics class 10 maths 2025 class 10 mathematics 2025-26 cbse class 10 maths cbse maths class 10 2025-26 class 10 maths term 1 2025 class 10 maths term 2 2026 class 10 maths syllabus 2025-26 cbse 2025 board exam class 10 class 10 maths important questions 2025 class 10 maths sample paper 2025 class 10 maths ncert solutions maths class 10 rd sharma cbse class 10 maths tips class 10th board exam 2025 class 10th maths preparation board exam 2025 class 10 maths cbse maths class 10 question paper mathematics class 10 cbse 2025 maths class 10 chapter wise maths tricks for class 10 how to score 100 in class 10 maths maths class 10 full syllabus