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Arithmetic Progression Class 10 in One Shot πŸ”₯ | Class 10 Maths Chapter 5 AP | Shobhit Nirwan

Shobhit Nirwan・100 minutes read

The video covers the Arithmetic Progression Chapter of Class 10th, highlighting the importance of studying AP for better comprehension through detailed explanations and examples. It encourages independent learning by posing questions from previous years and sample papers, advising viewers to refer to NCRT RD and RS questions for further practice and understanding the material thoroughly.

Insights

  • Arithmetic Progression (AP) is a crucial concept where each term is obtained by adding a fixed number (common difference) to the previous term, forming a sequence that can be analyzed for patterns and relationships.
  • Understanding AP involves calculating common differences between terms and applying formulas to determine specific terms, the sum of terms, and other related values, providing a structured approach to solving problems and analyzing sequences.
  • The application of AP extends beyond mathematical calculations to real-world scenarios like financial planning, production trends, and geometric constructions, showcasing the practical relevance and versatility of this fundamental concept in various contexts.

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Recent questions

  • What is Arithmetic Progression (AP)?

    A sequence with a constant difference between terms.

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Summary

00:00

Understanding Arithmetic Progression in Class 10

  • The video discusses the Arithmetic Progression Chapter of Class 10th, also known as AP.
  • The chapter receives many comments from children and is filled with sections.
  • Studying AP is recommended for a better understanding of the topic.
  • The concept will be clarified with each question.
  • After watching the video, viewers will be able to address questions from previous years and sample papers.
  • The chapter revolves around the definition of arithmetic progression.
  • The list of numbers in each term is obtained by adding a fixed number to the previous term.
  • The common difference between terms is explained as the next term minus the previous term.
  • The general form of AP is discussed, where each term is obtained by adding the common difference to the previous term.
  • Examples are provided to illustrate the application of common difference and the general form of AP.

11:43

"Calculating Common Differences to Verify A"

  • Adding zero to term two results in two
  • The sequence continues with twos
  • The process involves checking for common differences
  • Verification for the sequence being an A
  • Calculations for common differences in the sequence
  • The importance of common differences in determining A
  • Detailed calculations for common differences in the sequence
  • Verification process for confirming A
  • Application of common difference calculations for A verification
  • Solving a word problem to determine if the sequence is in AP

23:07

Vacuum Pump Removes Air in Cylinder

  • To indicate the amount of air present in a cylinder, a Vacuum Pump removes 1/4 of the air remaining in the cylinder at a time.
  • The initial air in the cylinder is considered as the starting point for the removal process.
  • Removing 1/4 of the air each time results in a new volume, such as 3v/4 after the first removal.
  • Continuing this process, the volume decreases to 9v/16 after multiple removals.
  • The remaining air in the cylinder after each removal is calculated by taking 1/4 of the current volume.
  • The formula for compound interest is principal * (1 + rate of interest)^time.
  • The amount left at the end of each year can be calculated using this formula.
  • The sequence of amounts left each year can be analyzed to determine if it forms an Arithmetic Progression (AP).
  • Checking for AP involves calculating the common difference between consecutive terms.
  • If the common difference remains constant, the sequence is in AP; otherwise, it is not.

35:09

"Sequencing Formula for Financial Planning Success"

  • Formula for calculating savings in FD at Rs. 7 with 7% interest rate after one year.
  • Encouragement to remember the formula for future financial planning.
  • Explanation of the formula's potential for creating one's own FD or investing in mutual funds.
  • Introduction to the concept of terms in a sequence, starting with a1, a2, a3, and so on.
  • Explanation of the formula for determining the nth term in a sequence.
  • Detailed breakdown of the formula with examples using common differences.
  • Application of the formula to find specific terms like a5, a20, and a50.
  • Demonstration of finding the 10th, 20th, and 100th terms in a sequence.
  • Utilization of the formula to determine the term where a value of -81 occurs.
  • Exploration of the formula's application in finding the number of terms in a given sequence.

47:32

Arithmetic Progression: Finding 'a' and 'd'

  • The value of 'a' in the sequence is 3.
  • To find the value of 'n - 1 * d', it is given that *3 = 111, resulting in 'n - 1 * 3' equaling 108.
  • Solving for 'n - 1', it is found to be 36.
  • There are 37 terms in the sequence.
  • The third term is 5, and the seventh term is 9.
  • Two equations are formed with two variables, 'a' and 'd', to find their values.
  • By solving the equations, 'a' is determined to be 3 and 'd' to be 1.
  • The sequence is checked to confirm if it is an arithmetic progression (AP).
  • The sequence is verified to be an AP, and formulas for 'a' are derived.
  • The 301st term of the sequence is calculated to be 151.

59:37

"Two-Digit Numbers Divisible by 3"

  • The first three two-digit numbers divisible by 3 are 12, 15, and 18.
  • The common difference between these numbers is 3.
  • The total number of two-digit numbers divisible by 3 between 12 and 99 is 29.
  • The last term in the sequence is 99.
  • By using the formula n-1 * d = 99 - 12, the value of n is calculated to be 29.
  • Therefore, there are 30 two-digit numbers divisible by 3 in the sequence.
  • The 11th term from the end of the sequence is -32.
  • Subba Rao started working in 1995 with a salary of Rs 5000.
  • His salary reached Rs 7000 in the 8th year, which was in 2002.
  • Subba Rao's salary in 2006 was Rs 7000.
  • The sum of the terms in an arithmetic progression can be calculated using the formula sn = n/2 * (2a + (n-1) * d).

01:12:20

Formulas for Calculating Series Sum and Terms

  • The formula for finding the sum of the first seven terms is to calculate 7/2 * 2a.
  • To determine the value of n, the sum of the seven terms is set equal to 7/2.
  • The formula for finding the difference between the third and second terms is 3 * 2.
  • By substituting values, the sum of the first seven terms is calculated to be 63.
  • The formula for finding the sum of the first a terms of a series is crucial.
  • To find a specific term, the sum up to the previous term is subtracted from the sum up to the desired term.
  • Two essential formulas to remember are n/2 * a p a and n/2 * a + a.
  • The formula for finding the sum of n terms is n/2 * a p a.
  • The sum of n terms is calculated to be 78 by solving the equation n/2 * 2a + n - 1 * d = 78.
  • The formula for finding the sum of the first n positive integers is n * n+1/2.

01:25:12

TV set production and spiral length analysis.

  • The formula for the production of TV sets is based on a fixed increase in production every year.
  • In the third year, 600 TV sets were produced, and in the seventh year, 700 sets were produced.
  • The common difference in production is fixed, with the third term being 600 and the seventh term being 700.
  • By solving equations, the value of the first term (A) is found to be 550 sets.
  • The production in the tenth year is calculated to be 775 TV sets.
  • The total production in the first seven years is determined to be 5575 TV sets.
  • The length of a spiral made up of 13 semi-circles is calculated by finding the sum of the circumferences of each semi-circle.
  • The common difference in the lengths of the semi-circles is found to be 2, leading to a total length of 91 units.
  • The total length of the spiral is determined to be 91 units, representing the sum of the lengths of the 13 semi-circles.
  • The process involves rotating between centers A and B, with the lengths of each semi-circle being calculated based on the radii and the number of rotations.

01:38:14

Promoting independent learning through conceptual questions.

  • Encourages independent learning by posing important and conceptual questions, referencing NCRT RD and RS questions, advising to solve them individually after referring to NCRT. Additionally, suggests watching a Trigonometry video and promises to bring the next chapter in a few days, emphasizing the importance of self-study and understanding the material thoroughly.
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