Arithmetic Progression (A.P.)
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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