Q. 54.4( 11 Votes )

The sum of the first n terms of an AP is given by Sn = (3n2 - n) . Find its

(i) nth term,

(ii) first term and

(iii) Common difference.

Answer :

(i) Let an be the nth term of the AP.

To find: an


Then an =Sn - Sn - 1


= (3n2 - n) - (3(n - 1)2 - (n - 1))


= (3n2 - n) - (3n2 + 3 - 6n - n + 1)


= 6n - 4


(ii) Since an = 6n - 4


For first term, n = 1


By putting n = 1 in the nth term, we get,


a1 = 6(1) - 4


= 2


a = 2


(iii) Put n = 2 in the nth term, we get


a2 = 6 × (2) - 4


= 12 - 4


= 8


Now common difference = d = a2 - a1


= 8 - 2


= 6


Common difference = 6


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