# 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.

(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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