Posts

Showing posts with the label Sequence & Series

Sequence & Series

  Sequence & Series: Comprehensive Notes and 100 Practice Questions with Answers 1. What are Sequences and Series? Sequence:  An ordered list of numbers following a specific pattern or rule. Each number is called a term. Sequences can be finite or infinite. Example: 2, 4, 6, 8, ... (even numbers) 1 2 3 5 . Series:  The sum of the terms of a sequence. Example: 2 + 4 + 6 + 8 + ... is a series 1 2 3 5 . 2. Types of Sequences A. Number Series (Missing/Wrong Terms) Number series  are sequences where each term follows a rule. You may be asked to find the next term, a missing term, or a wrong term. Example (Missing): 2, 4, 8, 16,  ?  (Answer: 32, as each term ×2) Example (Wrong): 3, 6, 12, 25, 48 (Here, 25 is wrong; should be 24) B. Arithmetic Progression (AP) Definition:  Each term after the first is obtained by adding a fixed number (common difference, d) to the previous term 1 2 3 6 7 . General term:   a n = a 1 + ( n − 1 ) d a n = a 1 + ( n − 1 )...