Basics Questions on Sequence & Series

Duration: 6 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on sequences and series, specifically focusing on arithmetic progressions (AP). The instructor, Yash Jain, begins by introducing the topic with a title card and then presents a series of problems to demonstrate the application of key formulas. The first problem asks for the sum of an AP with 12 terms, a first term of -19, and a last term of 36. The instructor writes down the formula for the sum of an AP, S_n = n/2 (a + a_n), and substitutes the given values to calculate the sum as 66. The second problem involves an AP with 17 terms, a first term of -20, and a last term of 28, which is solved using the same formula to find a sum of 136. The final problem is a multiple-choice question where the relationship 7 times the 7th term equals 11 times the 11th term is given, and the task is to find the 18th term. The instructor uses the general term formula, a_n = a + (n-1)d, to set up the equation 7(a+6d) = 11(a+10d), which simplifies to -4a = 68d, or a = -17d. Substituting this into the formula for the 18th term, a_18 = a + 17d, results in a_18 = -17d + 17d = 0. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an animated title card for a lesson on 'SEQUENCE & SERIES'. The screen displays a cartoon boy at a desk with a chalkboard that shows the formula for the sum of a series, S_N = a1 + a2 + a3 + ... + aN. The instructor, Yash Jain, is visible in a small window in the bottom right corner. The title card also includes the text 'Basic To Advance' and 'KNOWLEDGE GATE EDUCATOR'. The instructor then introduces the first problem: 'In an AP, there are 12 terms, the first term is -19 and last term is 36. Find the sum of AP?'. He begins to solve it by writing down the given values: AP, n=12, a=-19, a_n=36.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to solve the first problem. He writes the formula for the sum of an arithmetic progression: S_n = n/2 (a + a_n). He substitutes the values from the problem: S_12 = 12/2 (-19 + 36). He then performs the calculation: S_12 = 6 * 17, which equals 102. He then moves to the second problem: 'In an AP, there are 17 terms, the first term is -20 and last term is 28. Find the sum of AP?'. He writes down the values: AP, n=17, a=-20, a_n=28. He applies the same formula: S_17 = 17/2 (-20 + 28). He calculates: S_17 = 17/2 * 8 = 17 * 4 = 68. He then transitions to the third problem, a multiple-choice question: 'If 7 times of the seventh term of an AP is equal to 11 times its eleventh term, then the 18th term of the AP will be __'. He writes the given condition: 7a_7 = 11a_11.

  3. 5:00 – 6:23 05:00-06:23

    The instructor begins solving the third problem. He writes the general formula for the nth term of an AP: a_n = a + (n-1)d. He then expresses the 7th and 11th terms: a_7 = a + 6d and a_11 = a + 10d. He substitutes these into the given equation: 7(a + 6d) = 11(a + 10d). He expands the equation: 7a + 42d = 11a + 110d. He rearranges the terms to get: 7a - 11a = 110d - 42d, which simplifies to -4a = 68d. He then solves for a: a = -17d. The question asks for the 18th term, so he writes a_18 = a + 17d. He substitutes a = -17d into this formula: a_18 = -17d + 17d = 0. The video ends with a 'Thanks for Watching' screen.

The video presents a structured lesson on arithmetic progressions, progressing from basic sum calculations to a more complex problem involving the relationship between terms. The core teaching method is the step-by-step application of formulas. The first two problems demonstrate the direct use of the sum formula S_n = n/2 (a + a_n) with given values. The third problem requires a deeper understanding, using the general term formula a_n = a + (n-1)d to establish a relationship between the first term (a) and the common difference (d), which is then used to find a specific term. The key insight is that the 18th term is independent of the specific values of a and d, as the relationship forces it to be zero. This demonstrates a powerful problem-solving technique in algebra.

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