Demo: Short Tricks to Quickly Solve Problems of Sequence Series

Duration: 10 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: वृद्धि और विकास / Growth and Development, विकास के सिद्धांत / Theories of Development, Concept of Pedagogy, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a detailed tutorial on solving problems related to Sequence and Series, specifically focusing on finding the number of common terms between two Arithmetic Progressions (APs). The instructor, Yash Jain Sir, begins by introducing the fundamental concept of sequences and series, displaying the general summation formula Sn = a1 + a2 + ... + an. The core of the lesson involves a systematic method to identify common terms by first locating the initial common term and then determining the interval between subsequent common terms using the Least Common Multiple (LCM) of the differences of the two original sequences. The video demonstrates this technique through multiple examples, starting with simpler APs to build intuition before applying the method to more complex numerical problems. A key derivation presented is for calculating the number of terms n in an AP, rearranging the standard formula an = a + (n-1)d to solve for n as n = (l - a)/d + 1. This derived formula is then applied to the sequence of common terms to determine the total count, illustrating a practical shortcut for competitive exam preparation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an introduction to the topic of Sequence and Series, explicitly displaying the text 'SEQUENCE & SERIES' on screen. The instructor defines the general formula for the sum of a series as Sn = a1 + a2 + ... + an. The lesson immediately transitions to a specific problem statement: 'Q: FIND THE NUMBER OF COMMON TERMS'. Two arithmetic sequences are presented for comparison: Sequence A (17, 21, 25, 29...417) and Sequence B (16, 21, 26, 31...466). The instructor identifies the first common term as 21. Visual cues include a cartoon character reacting to math problems and text indicating the difficulty level as 'Basic To Advance'. The instructor begins explaining that finding common terms requires identifying a pattern, specifically looking at the differences between consecutive terms in each sequence to establish an interval for common values.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the method for finding subsequent common terms by calculating the Least Common Multiple (LCM) of the differences of the two sequences. For Sequence A, the difference is 4 (21-17), and for Sequence B, the difference is 5 (21-16). The LCM of 4 and 5 is calculated as 20. This value represents the interval between common terms. The instructor lists the sequence of common terms starting from 21: 21, 41 (21+20), 61 (41+20), and so on. A simpler example is introduced to clarify the concept, using APs with differences d=2 (2, 4, 6...) and d=3 (3, 6, 9...). The instructor visually circles common terms like 6, 12, and 18 in these sequences. This segment emphasizes the visual identification of common terms and the step-by-step breakdown using a simpler example to ensure understanding before moving to complex calculations.

  3. 5:00 – 9:37 05:00-09:37

    The video focuses on deriving and applying the formula to count the number of terms in the sequence of common terms. The instructor writes the standard nth term formula an = a + (n-1)d and algebraically rearranges it to isolate n, resulting in the formula n = (l - a)/d + 1. This derivation is shown step-by-step on the screen. The instructor then applies this formula to a specific problem involving the LCM of 2 and 3, calculating n = (18 - 6)/6 + 1. Returning to the main problem, the instructor identifies the first common term (a=21) and uses the LCM of differences (d=20) for the new sequence. The calculation begins with substituting values into the formula: n = (417 - 21) / 20. The instructor explains how to determine the last term of the common sequence that does not exceed the original limits (417 and 466) to accurately compute n. The segment concludes with the application of this derived formula to find the total count of common terms.

The instructional content follows a logical progression from definition to application. It begins by establishing the problem context: finding common terms between two Arithmetic Progressions (APs). The instructor first identifies the initial common term, which serves as the starting point for a new AP formed by these common terms. The critical insight provided is that the difference of this new sequence is the Least Common Multiple (LCM) of the differences of the original two sequences. For instance, with differences 4 and 5, the LCM is 20, creating a new sequence with a common difference of 20. To find the total count of these terms, the video derives the formula n = (l - a)/d + 1 from the standard nth term equation. This derivation is crucial for students to understand how to isolate n algebraically. The application involves determining the largest term in the common sequence that fits within the bounds of both original sequences. By substituting the first common term, the LCM-derived difference, and the maximum possible last term into the formula, students can efficiently calculate the number of common terms without listing them all. This method is presented as a shortcut for solving complex sequence problems quickly.

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