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Day 12- Arithmetic Progressions (AP) | Revision & Most Expected Questions | Shobhit Nirwan

Maths By Shobhit Nirwan・113 minutes read

A live interaction with various speakers, including Ogi Bhaiya, discussing topics like arithmetic progression, common differences, and formulas, emphasizing the simplicity and application of concepts in sequences. Detailed explanations and examples are provided, illustrating the process of identifying sequences, finding specific terms, and calculating the sum of terms in a sequence, emphasizing practice and understanding for better preparation.

Insights

  • The study of arithmetic progression involves sequences with equal common differences between terms.
  • The formula for the general form of an arithmetic progression is A, A + D, A + 2D, A + 3D, and so on, adding a common difference to each term.
  • To determine if a sequence is arithmetic progression, check if the common differences between consecutive terms are equal.
  • Finding the 'ith' term of an arithmetic progression involves substituting values into the formula 'a + n - 1 * d' to calculate specific terms.

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Recent questions

  • What is an arithmetic progression?

    A sequence with equal common differences.

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Summary

00:00

"Live Interaction, 14-Day Challenge, Arithmetic Progression"

  • The text involves a live interaction where individuals are conversing, including Saurav, Priyanka, Dinesh, Vinod, Damini, Suresh, Aastha, Farheen, and others.
  • Mention of someone needing to take a bath due to body odor.
  • Reference to an email being sent to someone.
  • Discussion about punctuality and arriving on time.
  • The text transitions to a 14-day challenge, currently on day 12, focusing on arithmetic progression.
  • The challenge involves heavy chapters and questions, with a commitment to completing it.
  • A new channel is mentioned, opened seven to nine days ago, reaching 100 subscribers.
  • Cake cutting and song reveals occurred during live classes.
  • The text delves into the study of arithmetic progression, emphasizing its simplicity and formula-based nature.
  • Definitions and explanations of arithmetic progression, common difference, and the importance of equal common differences in a sequence are detailed.

14:31

Identifying Arithmetic Progressions: Finding Common Differences

  • To determine if a sequence is A or not, check if the common differences are equal.
  • Ogi Bhaiya explains the process of checking if a sequence is A or not.
  • The method involves finding the common differences between consecutive terms.
  • If all common differences are equal, the sequence is A.
  • The common differences can be positive, negative, zero, rational, or irrational.
  • The general form of an arithmetic progression (AP) involves adding a common difference to each term.
  • The formula for the general form of an AP is A, A + D, A + 2D, A + 3D, and so on.
  • The process of finding the common difference involves subtracting the next term from the previous one.
  • In a practical example with taxi fares, adding a fixed amount for each kilometer determines if it's an AP.
  • MCQs are used to test understanding of AP concepts, focusing on finding common differences to identify sequences.

29:08

"Mastering MCQs: Finding 'p' in Sequences"

  • The speaker expresses frustration at making mistakes while teaching and solving MCQs.
  • Emphasis on finding the value of 'p' for a specific term 'A' based on common differences.
  • Detailed explanation of the pattern in terms of 'a' and 'd' for different terms.
  • The formula for the 'ith' term of 'A' is clearly explained.
  • The process of finding the 'eth' term of 'A' using the formula 'a + n - 1 * d' is outlined.
  • The importance of substituting values into the formula to find specific terms of 'A' is highlighted.
  • The speaker discusses the creation of a motivational song for children to aid in studying and staying motivated.
  • The process of solving linear equations to find the values of 'a' and 'd' for a given sequence is explained.
  • The practical application of the formula and solving linear equations to determine specific terms of 'A' is demonstrated.
  • The final calculation and verification of the 'eth' term of 'A' based on the derived values of 'a' and 'd' is illustrated.

43:34

"Finding A in Equations with MCQ"

  • Easy BG is a formula for finding the value of A.
  • Two equations were formed and solved in D using the formula A P A Mavdi.
  • An MCQ was presented with four options, requiring careful consideration within two minutes.
  • The question was similar to a previous one, emphasizing the need for the correct answer.
  • The 17th term of an AP was discussed, with the 17th term exceeding the 10th term by 7, leading to the common difference being calculated as 1.
  • The 109th term of an AP was determined to be the 22nd term.
  • The process of identifying unknown terms in a sequence was explained, with the 109th term being found to be the 37th term.
  • The concept of unknown terms in a sequence was further elaborated, with the 37th term being confirmed.
  • A term in a sequence was checked for the presence of -150, leading to the realization that it was not a valid term.
  • The process of verifying the existence of a term in a sequence was detailed, highlighting the importance of checking assumptions and calculations.

58:31

"Reversing Series to Find 10th Term"

  • The text discusses finding the 10th term of a series by reversing it and using a formula.
  • It emphasizes the process of reversing the series and calculating the 10th term from the end.
  • The formula a10 = a + (10 - 1) * d is used to determine the 10th term.
  • Specific numerical values are provided, such as a = 254 and d = -5, to calculate the 10th term.
  • The process involves reversing the series and applying the formula to find the 10th term.
  • The text highlights the importance of understanding formulas rather than memorizing them.
  • It transitions to discussing the divisibility of two-digit numbers by 3, starting from 10 to 99.
  • The process involves identifying numbers divisible by 3 and determining the total count of such numbers.
  • The text concludes by explaining the concept of middle terms in an arithmetic progression.
  • It outlines the formula for finding the middle term based on the number of terms in the series, whether odd or even.

01:12:43

Middle Term Position in Odd Number Sequence

  • The value of n is 7, making 7 an odd number.
  • The middle term is calculated as 7 + 1/2, resulting in 8.
  • The fourth term is identified as the middle term.
  • When Sis comes, the sixth and seventh terms are both middle terms.
  • The number of terms is determined to be 31.
  • The 16th term is established as the middle term.
  • The position of the middle term is sought, not its value.
  • The value of the 16th term is calculated as 111.
  • The equation aPm-1 - n = 0 is proven.
  • The proof involves showing that m is not equal to n.

01:27:57

"Mathematical Method to Solve Equations"

  • Children easily get nervous when asked questions
  • Aya Bhaiya Siya is a method to make questions difficult
  • Lack of concentration leads to problems
  • Moving on to the next topic, Sum of N terms
  • Formula for sum of N terms of A: n/2 * 2a + n - 1 * d
  • Example: Finding the sum of first 100 terms of A
  • Formula for finding unknown terms: n/2 * 2a + n - 1 * d = 180
  • Solving for the value of n in the equation
  • Taking 6 as a common factor in the equation
  • Final equation to find the value of n: 3n - 48n + 180 = 0

01:43:00

Calculating n in Quadratic Equation & Sequence

  • The value of n in a quadratic equation needs to be calculated.
  • To factorize, consider taking common factors.
  • Taking 6 as a common factor is a viable option.
  • By taking 6 as a common factor, the equation simplifies to n(n-6)(n-10) = 0.
  • To find the values of n, consider dividing 16 into two numbers whose sum is 16 and product is 160.
  • The two solutions for n are 6 and 10.
  • The concept of sum of terms in a sequence is explained.
  • The formula for finding the nth term from the sum of terms is discussed.
  • The sum of terms in a sequence is related to the nth term.
  • A complex question involving the sum of terms in a sequence is presented, requiring careful analysis and calculation.

01:57:24

Solving Equations for Variables P, A, D

  • The process involves solving the equation 2a प्पडी - d Paddi - d = 2q to find the values of p, a, and d.
  • Multiplying p inside the equation 2a p p s d - dp0 2q is a crucial step in the process.
  • Taking T inside the equation and multiplying p inside p is necessary for further calculations.
  • The equation involves variables p and q, with constants p and q being crucial for solving for the values of A and D.
  • Subtracting the second equation from the first equation leads to a new equation with 2a common and p - k common.
  • By taking d common out of the equation, a new form of the equation is derived, leading to further simplification.
  • The process involves taking p - q common throughout the equation to simplify and solve for the values of A and D.
  • The final step includes proving the equation by substituting values and ensuring that LHS equals RHS.
  • The speaker emphasizes the importance of practicing NCERT, solving previous year questions, and revising notes for better understanding and preparation.
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