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If the sum of first p terms of an A.P. ...

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

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To solve the problem, we need to find the sum of the first (p + q) terms of an arithmetic progression (A.P.) given that the sum of the first p terms is equal to the sum of the first q terms. ### Step-by-Step Solution: 1. **Formula for the Sum of n Terms of an A.P.**: The sum \( S_n \) of the first \( n \) terms of an A.P. can be expressed as: \[ S_n = \frac{n}{2} \left(2a + (n - 1)d\right) ...
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If the sum of the first 9 terms of an AP is equal to the sum of its first 11 terms, then find the sum of its first 20 terms.

If the sum of the first 9 terms of an AP is equal to the sum of its first 11 terms, then find the sum of its first 20 terms.

Knowledge Check

  • The sum of first p terms of an A.P. is q and the sum of the first q terms is p. The sum of the first (p + q) terms is

    A
    p + q
    B
    0
    C
    `- (p + q)`
    D
    `-2 (p + q)`

  • If sum of first 20 terms of an A.P. is equal to sum of first 30 terms of the A.P. then sum of the first 50 terms of the A.P. is

    A
    `-1`
    B
    0
    C
    10
    D
    25

  • If the first term of an AP is a and the sum of the first p terms is zero, then the sum of its next q terms is

    A
    `(a(P+q)q)/(p-1)`
    B
    `(-a(P+q)q)/(p-1)`
    C
    `(a(P-q)q)/(p-1)`
    D
    None of the above

    • Similar Questions

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    The sum of first p- terms terms of an A.P.is q and the sum of first q terms is p,find the sum of first (p+q)

    If the sum of first 10 terms of an A.P is 60 and sum of first 15 terms is -165 then find the sum of its n terms

    If the sum of first 6 terms of A.P.is 96 and sum of first 10 terms is 240 ,then find the sum of n terms of A.P.

    The sum of first 20 terms of an A.P. is one third of the sum of next 20 term. If first term is 1, find the sum of first 30 terms of this A.P.

    If the sum of the first 9 terms of an A.P. is 81 and that of the first 18 terms is 324, find the sum of its first n terms.

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