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) (l^{2} + 2^{2} + 3^{2} + ... + n^{2}) = n (n+1)(2n+1)/6
(iii) (1^{3} + 2^{3} + 3^{3} + ... + n^{3}) =n^{2}(n+1)^{2}

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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) (l

^{2}+ 2^{2}+ 3^{2}+ ... + n^{2}) = n (n+1)(2n+1)/6(iii) (1

^{3}+ 2^{3}+ 3^{3}+ ... + n^{3}) =n^{2}(n+1)^{2}