If the terms of a sequence follow some pattern that can be defined by an explicit formula in n, then the sequence is called a progression. There are some sequences that do not form any series even after finding the difference of successive terms they do not form any series . So, in that case, we use the Vn Method. In real life, we use the Vn Method for finding the sum of a special series.
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In this article, we will cover the Vn Method. This category falls under the broader category of sequence and series, which is a crucial Chapter in class 11 Mathematics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination(JEE Main) and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE, and more. Over the last ten years of the JEE Main Exam (from 2013 to 2023), a total of eleven questions have been asked on this concept, including two in 2013, two in 2021, four in 2022, and two in 2023.
The Vn method is finding the difference between two consecutive terms in terms of n and at the end only two terms that is one first term and one last term in terms of n are left.
d be the common difference of an AP, then
Example 1: If , then is equal to: [JEE MAINS 2023]
Solution: Given that
Hence, the answer is
Example 2: The sum is equal to [JEE MAINS 2022]
Solution: Required sum
Hence, the answer is
Example 3: is equal to: [JEE MAINS 2022]
Solution
Hence, the answer is 22! - 2. 21!
Example 4: If , then is equal to________ [JEE MAINS 2022]
Solution
Hence, the answer is the 286.
Example 5: If , then the maximum value of a is: [JEE MAINS 2022]
Solution
Hence, the answer is 212.
Vn method helps us to find the sum of special series that are neither in AP nor in GP. Understanding of Vn method helps us to know the pattern of the series and also enables us to find the general term of the sequence. This method remains valuable in computational mathematics for its ability to handle a wide range of sequences and series, enhancing our understanding and application of numerical techniques in mathematical analysis.
The Vn method is finding the difference between two consecutive terms in terms of n and at the end only two terms that is one first term and one last term in terms of n are left.
A geometric sequence is a sequence where the first term is non-zero and the ratio between consecutive terms is always constant. The ‘constant factor’ is called the common ratio and is denoted by ‘r’. r is also a non-zero number.
An arithmetic progression is a sequence in which each term increases or decreases by a constant term or fixed number. This fixed number is called the common difference of an AP and is generally denoted by ‘d’.
Answer: The sum, Sn of n terms of an AP with the first term ‘a’ and common difference ‘d’ is given by
Answer:
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