Q. 65.0( 10 Votes )

The sum of the first n terms of an AP is . Find the nth term and the 20th term of this AP.

Answer :

Let an be the nth term of the AP.

To find: an and a20


Since, an =Sn - Sn - 1


= ( ) - ()


= 1/2 (5n2 + 3n) - 1/2 [5(n - 1)2 + 3(n - 1)]


= 1/2 (5n2 + 3n - 5n2 - 5 + 10n - 3n + 3)


= 1/2 (10n - 2)


= 5n - 1


Since an = 5n - 1


For 20th term, put n = 20, we get,


a20 = 5(20) - 1


= 100 - 1


= 99


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