The nth term of an A.P. , the sum of whose nth term is Sn is....?expla

1.	The nth term of an A.P. , the sum of whose nth term is Sn is....?explain
Answer» We know, difference between two consecutive terms of an arithmetic progression (AP) must be same.e.g., if a is the first term and d is the common difference of an AP.then, series is : a , a + d , a + 2d , a + 3d , a + 4d...... are in APnow, nth term = = a + (n - 1)dsum of n terms = = a + (a + d) + (a + 2d) + ..... + [a + (n - 1)d]= (a + a + a ....n times ) + [d + 2d + 3d + .... + (n - 1)d ]= na + d[1 + 2 + 3 + ..... + (n -1)]= na + d[(n - 1)(n)/2 ]= n/2 [ 2a + (n - 1)d]hence, = n/2 [2a + (n - 1)d ] Sn=n/2+{2a+(n-1)d}

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