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The first term, last term and common dif...

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).`

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To prove that the sum of the arithmetic progression (A.P.) with first term \( a \), last term \( l \), and common difference \( d = 1 \) is given by \[ S = \frac{1}{2}(a + b)(1 - a + b), \] we will follow these steps: ...
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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) .

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Knowledge Check

  • If the first, second and the last terms of an A.P. are a,b,c respectively, then the sum of the A.P. is

    A
    `((a+b)(a+c-2b))/(2(b-a))`
    B
    `((b+c)(a+b-2c))/(2(b-a))`
    C
    `((a+c)(b+c-2a))/(2(b-a))`
    D
    none of these

  • The first term, second term and middle term of an A.P. are a, b and c respectively. The sum of this A.P. is :

    A
    `(2b(c-a))/(b-a)`
    B
    `(2a(a-b))/(b-c)`
    C
    `(2c(c-a))/(b-a)`
    D
    None of these

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