Class 10 Maths | Chapter 5: Arithmetic Progressions (समान्तर श्रेढ़ी) Exercise 5.3 & Exercise 5.4

NCERT Class 10 Maths | Chapter 5: Arithmetic Progressions (समान्तर श्रेढ़ी) Complete Step-by-Step Solutions: Exercise 5.3 & Exercise 5.4 (Optional) In this comprehensive lecture, we cover complete, step-by-step solutions for NCERT Class 10 Mathematics Chapter 5 - Arithmetic Progressions (AP) covering both Exercise 5.3 (Sum of n terms) and the advanced optional problem set in Exercise 5.4. Every concept, algebraic problem, and word problem is solved with clear explanations, shortcuts, cross-verification methods, and key board-exam tips to help you master this chapter and score 100% in CBSE and State Board exams! ⏱️ Timestamps: Exercise 5.3: Concept & Direct Sum Problems [00:00] - Introduction to Sum of an AP (S_n) & Core Formulas [01:30] - Ex 5.3, Q1 (i): Sum to 10 terms of 2, 7, 12, \dots [02:50] - Ex 5.3, Q1 (ii): Sum to 12 terms of -37, -33, -29, \dots [03:43] - Ex 5.3, Q1 (iii): Sum to 100 terms of 0.6, 1.7, 2.8, \dots [06:08] - Ex 5.3, Q1 (iv): Sum to 11 terms of \frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \dots [07:48] - Ex 5.3, Q2 (i): Find sum of 7 + 10\frac{1}{2} + 14 + \dots + 84 [10:12] - Ex 5.3, Q2 (ii): Find sum of 34 + 32 + 30 + \dots + 10 [11:20] - Ex 5.3, Q2 (iii): Find sum of (-5) + (-8) + \dots + (-230) Exercise 5.3: Algebraic Sub-questions (Question 3) [12:50] - Ex 5.3, Q3 (i): Given a=5, d=3, a_n=50, find n and S_n [13:52] - Ex 5.3, Q3 (ii): Given a=7, a_{13}=35, find d and S_{13} [15:12] - Ex 5.3, Q3 (iii): Given a_{12}=37, d=3, find a and S_{12} [15:54] - Ex 5.3, Q3 (iv): Given a_3=15, S_{10}=125, find d and a_{10} [17:16] - Ex 5.3, Q3 (v): Given d=5, S_9=75, find a and a_9 [19:07] - Ex 5.3, Q3 (vi): Given a=2, d=8, S_n=90, find n and a_n (Quadratic Equation) [22:51] - Ex 5.3, Q3 (vii): Given a=8, a_n=62, S_n=210, find n and d [26:14] - Ex 5.3, Q3 (viii): Given a_n=4, d=2, S_n=-14, find n and a [29:38] - Ex 5.3, Q3 (ix): Given a=3, n=8, S=192, find d [30:57] - Ex 5.3, Q3 (x): Given l=28, S=144, n=9, find a Exercise 5.3: Word Problems & Applications [33:31] - Ex 5.3, Q4: How many terms of 9, 17, 25, \dots give a sum of 636? [37:23] - Ex 5.3, Q5: First term 5, last term 45, sum 400 [38:37] - Ex 5.3, Q6: First term 17, last term 350, common diff 9 [42:12] - Ex 5.3, Q7: Find sum of first 22 terms (d=7, a_{22}=149) [43:27] - Ex 5.3, Q8: Sum of first 51 terms (a_2=14, a_3=18) [45:09] - Ex 5.3, Q9: If S_7=49 and S_{17}=289, find S_n [47:46] - Ex 5.3, Q10: Show a_n = 3 + 4n and a_n = 9 - 5n form an AP [53:17] - Ex 5.3, Q11: If S_n = 4n - n^2, find a_1, S_2, a_2, a_3, a_{10}, a_n [56:28] - Ex 5.3, Q12: Sum of first 40 positive integers divisible by 6 [57:52] - Ex 5.3, Q13: Sum of first 15 multiples of 8 [59:11] - Ex 5.3, Q14: Sum of odd numbers between 0 and 50 [01:02:53] - Ex 5.3, Q15: Construction contract delay penalty problem [01:05:33] - Ex 5.3, Q16: Seven cash prizes problem (Total ₹700) [01:08:16] - Ex 5.3, Q17: School tree plantation problem (Classes 1 to 12) [01:12:42] - Ex 5.3, Q18: Spiral made of 13 consecutive semicircles [01:16:49] - Ex 5.3, Q19: 200 logs stacked in rows [01:19:29] - Ex 5.3, Q20: Potato race problem Exercise 5.4: Optional (Advanced Problems) [01:23:04] - Ex 5.4, Q1: First negative term of 121, 117, 113, \dots & Inequalities concept [01:29:41] - Ex 5.4, Q2: Sum of 3rd & 7th term is 6, product is 8; find S_{16} [01:35:01] - Ex 5.4, Q3: Ladder rungs spacing & total wood length required [01:40:30] - Ex 5.4, Q4: Row of houses numbered 1 to 49 (Find house number x) [01:44:02] - Ex 5.4, Q5: Football ground terrace concrete volume problem [01:48:10] - Summary & Key Exam Tips 📌 Video Link: Watch the complete lecture here:    • Class 10 Maths | Chapter 5: Arithmetic Pro...   🏷️ Hashtags: #Class10Maths #ArithmeticProgression #NCERTSolutions #Exercise5_3 #Exercise5_4 #Class10Chapter5 #CBSEClass10 #MathsTutorial #BoardExam2027 #DhanabOnlineLecture Maths #Mathematics #Math #PureMathematics #AppliedMath #LoveMath #MathIsFun #MathGeek #MathNerd #MathTricks #DailyMath #MathDaily #MathHelp #MathSkills #MathematicsEducation #Geometry #EuclideanGeometry #GeometricShapes #Triangles #CircleTheorems #Educator #TeachingMath #TeacherLife #OnlineTutor #MathTutor #EducatorsOfInstagram #TeachersOfYouTube #Education #OnlineEducation #EdTech #SchoolEducation #STEMEducation #Class10Maths #Chapter6Triangles #SimilarTriangles #BPTTheorem #ThalesTheorem #BasicProportionalityTheorem #PythagorasTheorem #BaudhayanaTheorem #GeometryClass10 #NCERTMaths #CBSEClass10 #MathsTricks #Class10BoardExam #TrianglesClass10 #NCERTSolutions #CoordinateGeometry #CoordinateGeometryClass10 #DistanceFormula #SectionFormula #MidpointFormula #AreaOfTriangle #CollinearPoints #CartesianPlane #XaxisYaxis #QuadrantSystem #Algebra #AlgebraBasics #LinearEquations #QuadraticEquations #Polynomials #Arithmetic #ArithmeticProgression #APClass10 #APFormula #SumOfAP #NthTermOfAP #MathsFormulas #BoardExamPrep #MathsEducation #SchoolMaths #SecondaryMaths #Class10NCERT #ViralPathak #DhanabMaths #LearnMaths #MathTeacher #MathsLecture #TriangleTheorems