Let the first term be a and common difference be d.

Given that k^th term of the A.P. is 5k + 1.

k^th term = a_k = a + (k – 1)

∴ a + (k – 1)d = 5k + 1 ⇒ a + kd – d = 5k + 1

Comparing the coefficient of k, we obtain d = 5 and a – d = 1

⇒ a – 5 = 1

⇒ a = 6

Putting the value of a and d

∴