Class 11 Exam > Class 11 Questions > If Sn denotes the sum of first n terms of an ...
Start Learning for Free
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
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup