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If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this?
Most Upvoted Answer
If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2...
Solution:
Let a be the first term and d be the common difference of the given A.P.
Then, Sn = n/2[2a + (n-1)d] ...(1)
Now, S2n = 2n/2[2a + (2n-1)d] = n[2a + (2n-1)d] ...(2)
Also, S3n = 3n/2[2a + (3n-1)d] ...(3)
Now, S3n - Sn-1 = [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n(2a + (3n-1)d) - (n-1)(2a + (n-2)d)]/2
= [6an + 9n^2 - 3nd - 2a - nd + 2d]/2
= [9n^2 + 4d - 2]/2
= [9n^2 + 4d - 2]/2
= [9n^2 + 4d - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
=
Let a be the first term and d be the common difference of the given A.P.
Then, Sn = n/2[2a + (n-1)d] ...(1)
Now, S2n = 2n/2[2a + (2n-1)d] = n[2a + (2n-1)d] ...(2)
Also, S3n = 3n/2[2a + (3n-1)d] ...(3)
Now, S3n - Sn-1 = [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n/2[2a + (3n-1)d]] - [(n-1)/2[2a + (n-2)d]]
= [3n(2a + (3n-1)d) - (n-1)(2a + (n-2)d)]/2
= [6an + 9n^2 - 3nd - 2a - nd + 2d]/2
= [9n^2 + 4d - 2]/2
= [9n^2 + 4d - 2]/2
= [9n^2 + 4d - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
= [(3n)^2 + 2^2 - 2]/2
=
Community Answer
If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2...
Replace n by given cases as by 2n or 3n and get answer
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If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this?
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If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this?.
If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Sn denotes the sum of first n terms of an A.P then S3n-Sn-1 /S2n-S2n-1 is always equal to ? (a) 2n (b) 2n +1 (c)2n-1 (d)none of these Right answer is option (b) can you explain this?.
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