# nth term of a sequence is 2n + 1. Is this sequence an A.P.? If so find its first term and common difference.

We know that nth term of an A.P is given by,

an = a + (n – 1) d

Now equating it with the expression given we get,

2 n + 1 = a + (n – 1) d

2 n + 1 = a + nd – d

2 n + 1 = nd + (a – d)

Equating both sides we get,

d = 2 and a – d = 1

So we get,

a = 3 and d = 2.

So the first term of this sequence is 3, and the common difference is 2.

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