Short Tricks to Quickly Solve Problems of Sequence Series

Duration: 10 min

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This educational video, presented by Yash Jain from Knowledge Gate Educator, provides a comprehensive lesson on sequences and series, focusing on finding the number of common terms between two arithmetic progressions (APs). The video begins with an introduction to the topic, displaying the formula for the sum of a series, SN = a1 + a2 + a3 + ... + aN, and the title 'SEQUENCE & SERIES'. The main content is a worked example where the instructor analyzes two APs: A) 17, 21, 25, 29, ..., 417 and B) 16, 21, 26, 31, ..., 466. The core of the lesson involves identifying the common terms by first finding the Least Common Multiple (LCM) of the common differences (d=4 and d=5), which is 20. This LCM becomes the common difference of the new AP formed by the common terms. The instructor then uses the formula for the nth term of an AP, an = a + (n-1)d, to find the number of terms in this new sequence. The first common term is identified as 21, and the last common term is found to be 401. By substituting these values into the formula, the number of common terms is calculated as 20. 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 in a classroom setting, with a blackboard showing the formula for the sum of a series, SN = a1 + a2 + a3 + ... + aN. The instructor, Yash Jain, is introduced in a small window, and the channel name 'KNOWLEDGE GATE EDUCATOR' is visible. The overall theme is a 'Basic To Advance' course, setting the stage for a mathematical lesson.

  2. 2:00 – 5:00 02:00-05:00

    The video transitions to a problem-solving segment. The question 'q: FIND THE NUMBER OF COMMON TERMS' is displayed, with two arithmetic progressions listed: A) 17, 21, 25, 29, ..., 417 and B) 16, 21, 26, 31, ..., 466. The instructor begins to analyze the sequences, identifying the first common term as 21. He then calculates the common difference for each sequence, noting that the first sequence has a difference of 4 and the second has a difference of 5. He explains that the common terms will form a new arithmetic progression with a common difference equal to the LCM of 4 and 5, which is 20.

  3. 5:00 – 9:37 05:00-09:37

    The instructor demonstrates the final calculation. He establishes that the new AP of common terms has a first term (a) of 21 and a common difference (d) of 20. He then identifies the last common term, which is 401, by checking the last terms of the original sequences. Using the formula for the nth term, an = a + (n-1)d, he substitutes the values: 401 = 21 + (n-1)20. He solves for n, showing the steps: 380 = (n-1)20, which leads to n-1 = 19, and finally n = 20. The video concludes by confirming that there are 20 common terms between the two sequences.

The video presents a clear, step-by-step method for solving a common type of problem in sequences and series. It begins by establishing the context of arithmetic progressions and then applies a systematic approach: identifying the common difference of each sequence, finding the LCM to determine the common difference of the resulting sequence of common terms, and finally using the nth term formula to count the number of terms. The logical progression from identifying the first common term to calculating the total count provides a robust framework for students to solve similar problems.