Arithmetic Progression (A.P.)

Arithmetic Progression (A.P.)


  • Posted by  Smith 
    28 Jan, 2012

    If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P.
    An A.P. with first term a and common difference d is given by a, (a + d), (a + 2d),(a + 3d),.....
    The nth term of this A.P. is given by Tn =a (n - 1) d.
    The sum of n terms of this A.P.
    Sn = n/2 [2a + (n - 1) d] = n/2 (first term + last term).

    SOME IMPORTANT RESULTS :
    (i) (1 + 2 + 3 +. + n) =n(n+1)/2
    (ii) (l2 + 22 + 32 + ... + n2) = n (n+1)(2n+1)/6
    (iii) (13 + 23 + 33 + ... + n3) =n2(n+1)2

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