Series with combination

Duration: 12 min

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Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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, Network Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture introduces number and letter series, focusing on a difference-based trick for solving sequences. It presents three example series: 2, 5, 10, 17, 26, 37; 2, 6, 12, 20, 30, 42; and 0, 2, 6, 12, 20, 30. The instructor calculates first differences (e.g., +3, +5, +7 for the first series) and second differences to identify patterns. A key rule '±1 ±n' is highlighted, relating terms to index positions and base powers. The lesson then transitions to combination patterns like n²+1, n³-1, and cube-square combinations. A worked example shows 2, 5, 10, 17, 26, 37 as n²+1 (base squares 1,4,9,16,25,36 plus constant 1), yielding next term 7²+1=50. Another example works out 2, 9, 28, 65, 126 using cube gaps (1,8,27,64) with next value 125. The video concludes with a 'Series with Combination' slide listing ten patterns from Square+1 to Cube-Square, ending with 'THANKS FOR WATCHING'.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card 'NUMBER SERIES - LETTER SERIES' displaying the alphabet and digits, then transitions to a slide titled 'An Important Trick'. Three number series are presented: 2, 5, 10, 17, 26, 37; 2, 6, 12, 20, 30, 42; and 0, 2, 6, 12, 20, 30. A red check mark appears under the leading '2' of the middle series, followed by red difference values 4, 6, 8, 10, 12, 14 written beneath it with connecting check marks. The value '56' is handwritten in red into the middle series blank, and partial differences 2, 4, 6, 8 appear under the bottom series.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the difference method across all three series. For the first series, differences 3, 5, 7, 9, 11, 13 are written; for the second, 4, 6, 8, 10, 12; for the third, 2, 4, 6, 8, 10. A boxed rule '±1 ±n' is highlighted to guide pattern recognition. Index numbers 1, 2, 3, 4, 5, 6 are written below the first series, and a formula involving '±n' is applied to relate terms to their positions. Second-order differences of 2, 2, 2, 2 are calculated for both the first and third series, confirming constant second differences.

  3. 5:00 – 10:00 05:00-10:00

    The lesson shifts to combination patterns. Formulas such as n²+1, n³-1, and cube+square are listed. The series 2, 5, 10, 17, 26, 37 is broken into base squares (1, 4, 9, 16, 25, 36) with a constant +1 added to each, yielding the next term as 7²+1=50. The slide 'Series with Combination' lists ten patterns from 'Square + 1' to 'Cube - Square' alongside formulas like n²+1, n³-n, and n³-n². Red handwriting works out the series 2, 9, 28, 65, 126 with gaps 1, 8, 27, 64 and a next value 125.

  4. 10:00 – 12:09 10:00-12:09

    The final segment revisits the 'An Important Trick' slide, showing 2, 5, 10, 17, 26, 37 annotated in red with square-based differences and the form 'n² + (n)'. A drawing tool palette is visible on the left. The 'Series with Combination' slide reappears, listing ten patterns and formulas. A second row 0, 4, 18, 48, 106 is worked out alongside the cube-gap example. The video concludes with 'THANKS FOR WATCHING' on screen.

The lecture teaches a systematic approach to number series using first and second differences, then extends to combination patterns involving squares and cubes. The core method: compute consecutive differences; if first differences form an arithmetic progression (odd or even numbers), the second difference is constant. The '±1 ±n' rule connects terms to index positions, enabling formula-based solutions like n²+1. Worked examples demonstrate both the difference method (yielding 56 for the middle series) and the combination approach (yielding 50 for n²+1 and 125 for cube-gap series). The ten-pattern reference list provides a quick lookup for common combination types.

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