# the sum of n terms of a sequence is 3n2+4n.find the nth term and show that sequence is an A.p

Given, sum of n terms of the A.P., .

Replacing n by (n – 1) in , we get

Thus, the nth term of the A.P.  is 6n + 1.

A sequence is an A.P. if its  nth term is a linear expression in n. The  nth term of the given sequence is a linear expression in n, so the sequence is an A.P.

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The sum of n terms of an AP is given by a quadratic expression of degree 2. Twice the coefficient a2 is equal to the common difference. The first term 'a' is sum of first term or S1. So the first term is 3(1)^2+4(1) that is 7 And common difference is 3*2 i.e., 6.

So a=7 and d=6.

so an would be 7+(n-1)*6

1+6n

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