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The common difference of an A.P., the Sum of whose x terms is Sn, is
  • a)
    Sn - 2Sn-1 + Sn-2
  • b)
    Sn - 2Sn-1 - Sn-2
  • c)
    Sn - Sn-2
  • d)
    More than one of the above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The common difference of an A.P., the Sum of whose x terms is Sn, isa)...
Given :- Sum of x terms is 
Concept used :- nth term of an A.P. is 
As we know that :

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Most Upvoted Answer
The common difference of an A.P., the Sum of whose x terms is Sn, isa)...
Explanation:

1. Given: The sum of x terms of an arithmetic progression (A.P.) is Sn.
2. Let the first term of the A.P. be 'a' and the common difference be 'd'.
3. The sum of x terms of an A.P. is given by the formula: Sn = x/2 [2a + (x-1)d]
4. To find the common difference, we can manipulate the formula for Sn:
5. x/2 [2a + (x-1)d] = Sn
6. x(2a + d(x-1)) = 2Sn
7. 2ax + dx^2 - d = 2Sn
8. dx^2 + (2a-d)x - 2Sn = 0
9. This is a quadratic equation in terms of x.
10. To find the common difference, we can use the formula for the sum of x terms of an A.P.
11. The common difference of an A.P. can be calculated using the sum of x terms and the previous sums.
12. Therefore, the correct formula for the common difference is Sn - 2Sn-1 + Sn-2, which is option 'A'.
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