Series with combination

Duration: 12 min

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Inside: a video lesson and guided study material.

Module outline

  1. Aptitude: 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, Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, TCS NQT Advanced Quantitative Ability, Speed Mathematics and Basic Mathematics, Arithmetic, Statistics, Partnership, Age Problems, Mental Ability, Mensuration and Geometry, Linear Algebra, Calculus, Trigonometry, Vectors, Gamified / Game Based Aptitude
  2. Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, TCS NQT Advanced Reasoning Ability, Ranking, Order and Sequence, Analogy, Inequality, Data Arrangement, Venn Diagram, Logical Sequence Of Words, Selection Decision Table (Decision Making), Cubes & Dices, Clock, Calendar, Puzzle Solving (Puzzles), Analytical Reasoning (Counting Figures Reasoning), Directions (Direction Test), Blood Relations, Seating Arrangements
  3. Verbal Ability (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Articles, Direct and Indirect Speech, Conjunction, Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Verb
  4. Mega Test:
  5. Grand 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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