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Needed a Document for 1 Mark's questions of an arithematic progressio...
**Chapter 5 - Arithmetic Progressions, Class 10 Mathematics**
**Exercise 1: 1 Mark Questions**
1. **Question:** Find the sum of the first n natural numbers.
**Answer:**
The sum of the first n natural numbers can be found using the formula for the sum of an arithmetic series. In this case, we have an arithmetic series with a common difference of 1.
The formula for the sum of an arithmetic series is given by:
Sn = (n/2) * [2a + (n-1)d]
Where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, the first term (a) is 1 and the common difference (d) is also 1. Therefore, the formula simplifies to:
Sn = (n/2) * [2 + (n-1)]
Simplifying further, we have:
Sn = (n/2) * [n + 1]
So, the sum of the first n natural numbers is given by (n/2) * (n + 1).
2. **Question:** Find the sum of the first 20 odd natural numbers.
**Answer:**
To find the sum of the first 20 odd natural numbers, we can use the formula for the sum of an arithmetic series. In this case, we have an arithmetic series with a common difference of 2 (as the numbers are odd).
The first term (a) is 1, and the common difference (d) is 2. The number of terms (n) is 20.
Using the formula for the sum of an arithmetic series:
Sn = (n/2) * [2a + (n-1)d]
Substituting the values:
Sn = (20/2) * [2(1) + (20-1)(2)]
Simplifying further:
Sn = 10 * [2 + 38]
Sn = 10 * 40
Sn = 400
Therefore, the sum of the first 20 odd natural numbers is 400.
3. **Question:** Find the sum of the odd numbers between 0 and 20.
**Answer:**
To find the sum of the odd numbers between 0 and 20, we need to identify the first term and the last term of the series.
The first odd number is 1, and the last odd number before 20 is 19.
We can use the formula for the sum of an arithmetic series to find the sum.
The first term (a) is 1, the common difference (d) is 2 (as the numbers are odd), and the number of terms (n) is (19-1)/2 + 1 = 10.
Using the formula for the sum of an arithmetic series:
Sn = (n/2) * [2a + (n-1)d]
Substituting the values:
Sn = (10/2) * [2(1) + (10-1)(2)]
Simplifying further:
Sn = 5 * [2 + 18]
Sn = 5 * 20
Sn = 100
Therefore, the sum of the odd numbers between 0 and 20 is 100.
These are the solutions to the 1-mark questions in Exercise 1 of Chapter 5
**Exercise 1: 1 Mark Questions**
1. **Question:** Find the sum of the first n natural numbers.
**Answer:**
The sum of the first n natural numbers can be found using the formula for the sum of an arithmetic series. In this case, we have an arithmetic series with a common difference of 1.
The formula for the sum of an arithmetic series is given by:
Sn = (n/2) * [2a + (n-1)d]
Where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, the first term (a) is 1 and the common difference (d) is also 1. Therefore, the formula simplifies to:
Sn = (n/2) * [2 + (n-1)]
Simplifying further, we have:
Sn = (n/2) * [n + 1]
So, the sum of the first n natural numbers is given by (n/2) * (n + 1).
2. **Question:** Find the sum of the first 20 odd natural numbers.
**Answer:**
To find the sum of the first 20 odd natural numbers, we can use the formula for the sum of an arithmetic series. In this case, we have an arithmetic series with a common difference of 2 (as the numbers are odd).
The first term (a) is 1, and the common difference (d) is 2. The number of terms (n) is 20.
Using the formula for the sum of an arithmetic series:
Sn = (n/2) * [2a + (n-1)d]
Substituting the values:
Sn = (20/2) * [2(1) + (20-1)(2)]
Simplifying further:
Sn = 10 * [2 + 38]
Sn = 10 * 40
Sn = 400
Therefore, the sum of the first 20 odd natural numbers is 400.
3. **Question:** Find the sum of the odd numbers between 0 and 20.
**Answer:**
To find the sum of the odd numbers between 0 and 20, we need to identify the first term and the last term of the series.
The first odd number is 1, and the last odd number before 20 is 19.
We can use the formula for the sum of an arithmetic series to find the sum.
The first term (a) is 1, the common difference (d) is 2 (as the numbers are odd), and the number of terms (n) is (19-1)/2 + 1 = 10.
Using the formula for the sum of an arithmetic series:
Sn = (n/2) * [2a + (n-1)d]
Substituting the values:
Sn = (10/2) * [2(1) + (10-1)(2)]
Simplifying further:
Sn = 5 * [2 + 18]
Sn = 5 * 20
Sn = 100
Therefore, the sum of the odd numbers between 0 and 20 is 100.
These are the solutions to the 1-mark questions in Exercise 1 of Chapter 5
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Needed a Document for 1 Mark's questions of an arithematic progression? Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Needed a Document for 1 Mark's questions of an arithematic progression? Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Needed a Document for 1 Mark's questions of an arithematic progression? Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics?.
Needed a Document for 1 Mark's questions of an arithematic progression? Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Needed a Document for 1 Mark's questions of an arithematic progression? Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Needed a Document for 1 Mark's questions of an arithematic progression? Related: Exercise 1 - Chapter 5 - Arithmetic Progressions, Class 10, Mathematics?.
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