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Arithmetic Progression FULL CHAPTER | Class 10th Mathematics | Chapter 5 | Udaan

UDAAN・195 minutes read

Understanding number sequences involves identifying patterns and positions of specific terms, with formulas like a + (n-1)d utilized to calculate terms within sequences. Arithmetic progressions entail adding common differences to terms, with formulas like n/2 * [2a + (n-1) * d] used to determine the sum of terms within sequences.

Insights

Sequences convey meaning through specific number patterns.
Patterns in numbers help understand sequences.
Terms in a sequence are numbers in a specific order.
Formulas like a + (n-1)d help find specific terms in a sequence.
Arithmetic sequences involve adding a common difference to each term.
Understanding the relationship between variables is crucial in solving equations in arithmetic progression.

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Recent questions

What is an arithmetic sequence?
A sequence with a common difference between terms.
How do you find the nth term in an arithmetic sequence?
Use the formula a + (n-1)d.
What is the general term of an arithmetic progression?
The formula is a + (n-1)d.
How do you calculate the sum of terms in a sequence?
Use the formula n/2 * [2a + (n-1) * d].
What is the significance of the common difference in an arithmetic sequence?
It determines the pattern of the sequence.

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Summary

00:00

Understanding Number Sequences

Sequence is about numbers written in a specific pattern to convey meaning.
The term at a specific position in a sequence signifies a particular number.
The sequence can be understood by observing patterns in numbers.
Multiples of two are part of a sequence, like 2, 4, 6, etc.
Squares of natural numbers can form a sequence, like 1, 4, 9, 16, etc.
Not all number patterns form a sequence; a pattern must be discernible.
Terms in a sequence are the numbers written in a specific order.
The first term in a sequence is denoted as a1, the second as a2, and so on.
The position of a term in a sequence can be identified by its numerical designation.
The general term in a sequence helps determine any term's position in the sequence.

13:13

Finding nth term in arithmetic sequence formula

To find the nth term in a sequence, replace n with the desired term number.
For example, to find the third term, substitute n with 3.
Calculate the term by following the formula: a1 + (n-1)d.
The first term is obtained by replacing n with 1.
The second term is calculated by replacing n with 2.
The third term is found by substituting n with 3.
The formula for the nth term in an arithmetic sequence is a + (n-1)d.
The common difference between consecutive terms is denoted by d.
The next term in the sequence is obtained by adding the common difference to the previous term.
The pattern in an arithmetic sequence involves adding the common difference to each term to find the next term.

27:39

Finding Terms in Arithmetic Progressions

The formula for the seventh term is discussed, with a mention of a plus and minus value.
The method to calculate the 10th term is explained.
Instructions on how to determine the 15th term and the formula for PS 14D are provided.
The process of finding the general term of A is detailed.
The formula for the general term of any AP is clarified.
Steps to find the first term are outlined, including the calculation for A1, A2, A3, and A4.
The concept of common difference between terms is explained, emphasizing the importance of subtraction.
The method to identify common difference between terms is elaborated.
The process of finding the general term of a sequence is discussed, with examples of A1, A2, and A3.
The formula for the 15th term is demonstrated, highlighting the use of A + 14D.

41:19

Understanding Arithmetic Progressions and Finding Terms

The sequence involves a series of calculations based on adding multiples of 3 to a starting number.
The progression follows a pattern where each term is obtained by adding 3 to the previous term.
The concept of arithmetic progression is introduced, emphasizing the importance of understanding the first term and common difference.
The formula for finding the nth term in an arithmetic progression is explained as a + (n-1)d.
Practical examples are provided to illustrate the application of the formula in finding specific terms in the sequence.
The process of determining the nth term is detailed, involving substituting known values for the first term and common difference.
The calculation of specific terms, such as the 12th and 24th terms, is demonstrated using the formula.
The concept of finding terms from the end of a sequence is introduced, requiring a reversal of the sequence to determine specific terms.
Practical examples are given to clarify the process of finding terms from the end of a sequence.
The importance of understanding the concept of finding terms from the end of a sequence is emphasized through practical exercises.

55:06

Finding the 10th Term in AP

To find the 10th term, use the formula a10 = a + 9d, with a = 254 and d = -5, resulting in a10 = 254 - 45 = 209.
The 10th term in an arithmetic progression (AP) refers to the 10th term from the end of the sequence.
When determining the term from the end of an AP, reverse the sequence and consider the term's position from the end.
In the sequence provided, the 9th term is 18, leading to the 10th term being 209.
The position of a term in an AP can be calculated by understanding the sequence's structure and the term's value.
The last term in an AP can be identified by determining the position of the term in the sequence.
In the given sequence, the 31st term is 111, indicating there are 31 terms in the sequence.
To find the position of the last term in an AP, equate the term's value to the position to determine the total number of terms.
By setting the 37th term as 111, it is established that there are 37 terms in the sequence.
To solve for the first term and common difference in an AP, create equations using the given term values and relationships.

01:09:31

"Finding Terms in Arithmetic Progressions"

The task is to find a term in an arithmetic progression (AP) that is 130 more than the 31st term.
It is determined that the 8th term is indeed 130 more than the 31st term.
The equation is set up to solve for the term that is 130 more than the 31st term.
By substituting values, it is calculated that the value of n is 44.
The sum of the 5th and 9th terms of the AP is given as 72.
The sum of the 7th and 12th terms of the AP is given as 97.
Two equations are formed to find the values of a and d in the AP.
Through elimination, the values of a and d are calculated as 6 and 5 respectively.
The sequence is analyzed to determine if the 184th term is present, concluding that it is not.
An equation is set up to prove that the 13th term of the AP is zero, with calculations showing it to be true.

01:24:37

"Finding Value in Variables and Divisibility"

To prove the value of a p 12d, a13 0 is necessary.
Understanding the use of different variables is crucial to extract value.
The equation + 12d 0 means a + 12 0, and a13 0 means a13 0.
The smallest three-digit number divisible by seven is 105, and the largest is 994.
To find how many three-digit numbers are divisible by seven, divide 999 by 7 to get 128.
The numbers divisible by seven between 10 and 999 are 105, 112, 119, and so on.
The total number of three-digit numbers divisible by seven is 128.
To find the middle term of a sequence, determine the total number of terms.
If the total number of terms is odd, there will be one middle term; if even, there will be two.
The middle term of 23 terms is the 12th term, which is 125.

01:39:22

Middle Term in Arithmetic Progression Calculation

The n + 1 / th term will be the middle term.
The question is related to homework in CBSE.
The ninth term of a is equal to 7 times the second term.
The concept of age difference is explained using equations.
Equations are formed to find the first term and common difference.
Two equations are needed to find A and D.
The total terms in the AP are 50, with the last term being 106.
The concept of finding any term in the AP is discussed.
The first negative term in the AP is identified.
Equations are solved to find the value of n.

01:54:56

Significance of First Negative Term in Sequences

Understanding the concept of negative terms in a sequence, where the first negative term will set the pattern for subsequent terms.
Explaining the significance of the first negative term in a sequence and how it affects the following terms.
Clarifying the pattern of positive and negative terms in a sequence based on the initial negative term.
Emphasizing the importance of identifying the first negative term in a sequence to determine the subsequent terms.
Exploring the concept of arithmetic progression and the meaning of terms in a sequence.
Detailing the process of finding the value of a term in a sequence using arithmetic progression formulas.
Demonstrating the calculation of terms in a sequence by substituting values into the arithmetic progression formula.
Highlighting the method of solving equations to determine the values of variables in a sequence.
Encouraging a step-by-step approach to solving complex equations in arithmetic progression.
Concluding with the importance of understanding arithmetic progression concepts for solving mathematical problems effectively.

02:09:52

Solving Equations and Summing Sequences with Formulas

The text discusses simplifying mathematical equations involving variables like 'a', 'n', 'd', and 'm'.
It emphasizes the importance of understanding the relationship between these variables in equations.
The text delves into the concept of factorization and the significance of common differences in equations.
It explains the process of deriving formulas for the sum of 'n' terms in a sequence.
The text highlights the formula for finding the sum of 'n' terms as n/2 * [2a + (n-1) * d].
It provides practical examples of applying the formula to calculate the sum of terms in a sequence.
The text introduces another formula for finding the sum of 'n' terms as n/2 * [a + l], where 'l' represents the last term.
It demonstrates how to calculate the sum of terms in a sequence by substituting values into the formula.
The text presents a problem-solving approach to finding the sum of terms in a sequence by using given information and equations.
It concludes by illustrating the application of formulas to determine the sum of terms in a sequence, emphasizing the importance of understanding the relationships between variables.

02:24:27

Calculating Series Sum Terms with Formulas

Understanding the meaning of terms in a given ratio is crucial, such as a 10 38 and a 30.
Calculating the first and 13th term of a series involves finding the values of a1 and a13.
The formula n/2 is essential for determining the value of terms in a series.
Solving equations to find the values of A and D is necessary for calculating specific terms.
The process of finding the sum of three-digit natural numbers divisible by a certain number is explained.
Identifying the range of three-digit numbers divisible by a specific number is crucial for sum calculation.
Utilizing formulas and equations to determine the number of terms required for a specific sum is detailed.
Solving quadratic equations to find the value of n in a series is a key step in sum calculation.
The importance of understanding the concept of zero terms in a series for accurate sum calculation is highlighted.
Demonstrating the process of calculating the sum of terms in a series through practical examples and equations.

02:39:31

Finding Sums of Arithmetic Sequences

The sum of 18 terms is 513, indicating no difference in understanding with the addition of a term.
A question is posed regarding the sum of the first 'a' terms in a sequence, with the goal of finding the eighth term.
The concept of replacing 'n' with different values to find the sum of terms is explained.
The sum of one term is calculated by replacing 'n' with 1, resulting in the first term.
To find the sum of two terms, 'n' is replaced with 2, leading to the sum of the first two terms.
The process of replacing 'n' with different values to find the sum of any number of terms is detailed.
Understanding the sum of one term as the first term and the sum of two terms as the sum of the first two terms is emphasized.
A question is presented involving the last term being 29 and the sum of terms being 155, requiring the determination of the common difference 'd'.
The assumption of 'n' terms in the sequence to calculate the sum of terms is explained, leading to the identification of the last term.
The method of solving equations with two variables, 'n' and 'd', to find their values is demonstrated.

02:53:13

Finding the Sum of Arithmetic Sequences

The sum of the first 10 terms is 150.
The next 10 terms are from A11 to A20.
The sum is given from A11 to A20.
The sum of the next 10 terms is to be understood.
The sum of the first 20 terms is to be found.
Subtracting the sum of the first 10 terms will yield the next 10 terms.
The sum of the next 10 terms is to be understood.
Equations need to be written to solve for A and D.
The sum of the three middlemost terms is 225.
The sum of the last three terms is 429.

03:08:17

Sequences, Equations, and Calculations Explained

The formula n / 2 is used to derive the sequence.
The value of a is replaced by 2 plus n-1 d.
The equation 287 * 2 is solved to get 574.
The quadratic equation 3n - 574 = 0 is formed.
The discriminant is calculated to be 6889.
The process of determining if a number is a perfect square is explained.
The formula for finding the value of a term in a sequence is detailed.
The number of apples in different baskets is calculated based on given information.
The sum of apples in multiple baskets is determined using the formula for the sum of terms.
The process of repaying a loan in increasing installments is described.

03:23:03

Understanding Installments and Terms in Arithmetic Progressions

The text discusses the concept of installments and terms in an arithmetic progression (AP).
It mentions the importance of understanding the meaning of the fourth term in an AP.
The text delves into finding the amount paid in specific installments, such as the 28th installment.
It emphasizes the relationship between installments and terms in an AP, like the 20th installment corresponding to the 20th term.
The text includes calculations involving given amounts in installments, like 13000 and 19.
It highlights the process of determining the total amount paid by an individual over a certain period.
The text introduces the idea of returning a total amount in a specific number of installments.
It discusses the practical application of AP concepts in scenarios involving the production of TV sets over several years.
The text presents a problem involving the placement of logs in rows over consecutive days, requiring the calculation of the total number of days needed to place 200 logs.
It concludes with a quadratic equation problem related to determining the number of days required to place a specific number of logs daily.

03:38:16

"Sequence formula reveals answer in 16 days"

The answer will be available in 16 days, with a possibility of 25 days.
If 200 logs are kept, the work cannot be completed in 25 days.
The correct answer is 16, not 25.
The number of logs in 25 rows is calculated.
The value of x in an equation is determined to be 15/2.
The relationship between terms in a sequence is explained.
The formula for finding the nth term in a sequence is discussed.
The formula for the sum of n terms in a sequence is provided.

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