nth term of a sequence is 2n + 1. Is this sequence an A.P.? If so find

1.	nth term of a sequence is 2n + 1. Is this sequence an A.P.? If so find its first term and common difference.
Answer» We know that nth term of an A.P is given by, a_n = 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.

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

Answer»

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

a_n = 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.