Points to Remember
If a and b are two positive integers then there exist unique integers q and r such that a = bq + r, 0 ≤ r < |b|
Every composite number can be expressed as a product of primes and this factorization is unique except for the order in which the prime factors occur.
(i) Arithmetic Progression is a , a + d , a + 2d , a + 3d,….nth term is given by tn = a + (n −1)d
(ii) Sum to first n terms of an A.P. is
(iii) If the last term l (nth term is given, then Sn = )
(i) Geometric Progression is a , ar , ar2 ,….,arn−1 . nth term is given by tn= ar n−1
(ii) Sum to first n terms of an G.P. is
(iii) Suppose r =1 then S n = na
(iv) Sum to infinite terms of a G.P. a + ar + ar2 + is Where –1< r < 1
(i) The sum of first n natural numbers 1 + 2 + 3 + + n =
(ii) The sum of squares of first n natural numbers
(iii) The sum of cubes of first n natural numbers
(iv) The sum of first n odd natural numbers 1 + 3 + 5 + .... .. + (2n − 1) = n2
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