If the sum of n terms of an A. P. be 3n2 + n and the common difference is 6, then its 1st term is:

Given:

The sum of n terms of an A.P. is given by:

S_n = 3n² + n

The common difference, d = 6

Formula used:

The sum of the first n terms of an A.P. is given by the formula:

S_n = n/2 × (2a + (n - 1)d)

Where, a = first term, d = common difference

Calculations:

We are given S_n = 3n² + n, and d = 6. We can equate this to the formula for the sum of n terms of an A.P.:

3n² + n = n/2 × (2a + (n - 1) × 6)

Multiply both sides by 2 to eliminate the fraction:

6n² + 2n = n × (2a + 6n - 6)

Now, divide both sides by n (n ≠ 0):

6n + 2 = 2a + 6n - 6

Cancel out 6n from both sides:

2 = 2a - 6

2a = 8

a = 4

∴ The first term of the A.P. is 4.