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If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by?
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If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P...
Question: If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S1 ÷ (S2 -S3) is given by?
Solution:
To solve this problem, we need to first find the formulas for S1, S2, and S3:
Formula for Sum of n terms of an A.P:
Sn = n/2[2a + (n-1)d]
Where,
Sn = Sum of n terms
a = First term
d = Common difference
Formula for S1:
S1 = n/2[2a + (n-1)d]
Formula for S2:
S2 = 2n/2[2a + (2n-1)d]
Simplifying this equation, we get:
S2 = n[2a + (2n-1)d]
Formula for S3:
S3 = 3n/2[2a + (3n-1)d]
Simplifying this equation, we get:
S3 = (3n/2)[2a + (3n-1)d]
Now, substituting the formulas of S1, S2, and S3 in the expression S1 ÷ (S2 -S3), we get:
S1 ÷ (S2 -S3) = [n/2[2a + (n-1)d]] / {[n[2a + (2n-1)d]] - [(3n/2)[2a + (3n-1)d]]}
Simplifying this expression, we get:
S1 ÷ (S2 -S3) = [2/3(2n-1)]
Therefore, the value of S1 ÷ (S2 -S3) is [2/3(2n-1)].
Conclusion:
Thus, the solution to the given problem is [2/3(2n-1)].
Solution:
To solve this problem, we need to first find the formulas for S1, S2, and S3:
Formula for Sum of n terms of an A.P:
Sn = n/2[2a + (n-1)d]
Where,
Sn = Sum of n terms
a = First term
d = Common difference
Formula for S1:
S1 = n/2[2a + (n-1)d]
Formula for S2:
S2 = 2n/2[2a + (2n-1)d]
Simplifying this equation, we get:
S2 = n[2a + (2n-1)d]
Formula for S3:
S3 = 3n/2[2a + (3n-1)d]
Simplifying this equation, we get:
S3 = (3n/2)[2a + (3n-1)d]
Now, substituting the formulas of S1, S2, and S3 in the expression S1 ÷ (S2 -S3), we get:
S1 ÷ (S2 -S3) = [n/2[2a + (n-1)d]] / {[n[2a + (2n-1)d]] - [(3n/2)[2a + (3n-1)d]]}
Simplifying this expression, we get:
S1 ÷ (S2 -S3) = [2/3(2n-1)]
Therefore, the value of S1 ÷ (S2 -S3) is [2/3(2n-1)].
Conclusion:
Thus, the solution to the given problem is [2/3(2n-1)].
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If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by?
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If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by?.
If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If S1, S2, S3 be the respectively the sum of terms of n, 2n, 3n an A.P. the value of S 1 ÷ (S 2 -S 3 ) is given by?.
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