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The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?
- a)S1 + S3 = 2S2
- b)S1 - S3 = S2
- c)S1 + S2 = S3
- d)S1 + S3 + = S2
Correct answer is option 'A'. Can you explain this answer?
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The sum of n terms of the three arithmetic progression are S1, S2, S3....
Arithmetic Progression
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. The first term is denoted by 'a' and the common difference is denoted by 'd'.
Given Information
In this question, we have three arithmetic progressions with the following information:
- First term of each AP is unity (1).
- The common differences are 1, 2, and 3 for the three APs respectively.
Finding the Sum of n terms
The sum of the first 'n' terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Where:
- Sn is the sum of the first 'n' terms.
- a is the first term of the AP.
- d is the common difference.
- n is the number of terms.
Calculating S1, S2, and S3
Let's calculate S1, S2, and S3 using the given information.
S1 = (1/2)(2(1) + (1-1)(1)) = 1
S2 = (1/2)(2(1) + (1-1)(2)) = 3
S3 = (1/2)(2(1) + (1-1)(3)) = 6
Comparing the Options
Now, let's compare the options to find the correct one.
a) S1 + S3 = 1 + 6 = 7
2S2 = 2(3) = 6
Since S1 + S3 ≠ 2S2, option A is incorrect.
b) S1 - S3 = 1 - 6 = -5
S2 = 3
Since S1 - S3 ≠ S2, option B is incorrect.
c) S1 + S2 = 1 + 3 = 4
S3 = 6
Since S1 + S2 ≠ S3, option C is incorrect.
d) S1 + S3 = 1 + 6 = 7
S2 = 3
Since S1 + S3 ≠ S2, option D is incorrect.
Correct Answer
Based on the calculations and comparisons, none of the given options is correct.
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. The first term is denoted by 'a' and the common difference is denoted by 'd'.
Given Information
In this question, we have three arithmetic progressions with the following information:
- First term of each AP is unity (1).
- The common differences are 1, 2, and 3 for the three APs respectively.
Finding the Sum of n terms
The sum of the first 'n' terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Where:
- Sn is the sum of the first 'n' terms.
- a is the first term of the AP.
- d is the common difference.
- n is the number of terms.
Calculating S1, S2, and S3
Let's calculate S1, S2, and S3 using the given information.
S1 = (1/2)(2(1) + (1-1)(1)) = 1
S2 = (1/2)(2(1) + (1-1)(2)) = 3
S3 = (1/2)(2(1) + (1-1)(3)) = 6
Comparing the Options
Now, let's compare the options to find the correct one.
a) S1 + S3 = 1 + 6 = 7
2S2 = 2(3) = 6
Since S1 + S3 ≠ 2S2, option A is incorrect.
b) S1 - S3 = 1 - 6 = -5
S2 = 3
Since S1 - S3 ≠ S2, option B is incorrect.
c) S1 + S2 = 1 + 3 = 4
S3 = 6
Since S1 + S2 ≠ S3, option C is incorrect.
d) S1 + S3 = 1 + 6 = 7
S2 = 3
Since S1 + S3 ≠ S2, option D is incorrect.
Correct Answer
Based on the calculations and comparisons, none of the given options is correct.
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The sum of n terms of the three arithmetic progression are S1, S2, S3....
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The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer?
Question Description
The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer? 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 The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer?.
The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer? 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 The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of n terms of the three arithmetic progression are S1, S2, S3. The first term of each arithmetic progression is unity. The common differences are 1, 2, 3 respectively, then which of the following options is correct?a)S1 + S3 = 2S2b)S1 - S3 = S2c)S1 + S2 = S3d)S1 + S3 + = S2Correct answer is option 'A'. Can you explain this answer?.
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