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

Posted by Pachu Sona 6 years ago

CBSE > Class 10 > Mathematics

2 answers

Jayesh King 6 years ago

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 AP now, nth term = = a + (n - 1)d sum 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 ]

1Thank You

The King ?? ( Never Give Up ) 6 years ago

Sn=n/2+{2a+(n-1)d}

0Thank You

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