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Common difference of an A.P. is always p...

Common difference of an A.P. is always positive.

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The first term, last term and common difference of an A.P. are respectively a, b and 1. Prove that the sum of this A.P. is (1)/(2)(a+b)(1-a+b) .

The first term, last term and common difference of an A.P are respectively a, l and 1. Prove that the sum of this A.P. is (1)/(2)(a+b)(1-a+b).

Knowledge Check

  • The sum of the fist ten terms of an A.P. , equals 155 and the sum of the first two terms of a G.P. equals 9. The first term of the A.P. is equal to the common ratio of the G.P. and the common difference of the A.P. is equal to the first term G.P.. Give that the common difference of the A.P. is less then unity, which of the following is correct ?

    A
    `(25)/(2)` is a term of the G.P.
    B
    `(28)/(3)` is a term of the G.P.
    C
    `(28)/(3)` is a term of the A.P.
    D
    `(25)/(2)` is a term of the A.P.

  • Assertion (A) : If the n^(th) term of an A.P. is 7- 4n, then its common differences is -4. Reason (R ) : Common differences of an A.P .is given by d=a_(n+1)-a_(n)

    A
    Both A and R are true and R is the correct explanation for A.
    B
    Both A and R are true and R is not correct explanation for A.
    C
    A is true but R is false.
    D
    A is false but R is true.

  • The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. which can be the A.P. as per the given conditions?

    A
    2,4,6,8,10,.....
    B
    25/2,79/6,83/6, .....
    C
    2,5,8,11,.....
    D
    both (b) and (c)

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    The common difference of an A.P. 6, then a_(15) - a_(11) …….. .

    The common difference of an A.P. 6, then a_(15) - a_(11) …….. .

    Find the common difference of the A.P., if a=100and t_(20)=176 .

    The sum of first ten terms of an A.P. is equal to 155, and the sum of the first two terms of a G.P. is 9, if the first term of A.P. is equal to common ratio of G.P. and the first term of G.P. is equal to common difference of A.P. then these progressions are...................and..................

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