Demo: Short Tricks to Quickly Solve Problems of Sequence Series

Duration: 10 min

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Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
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  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends, Internet of Things
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
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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