If the first term of an A.P. is -18 and its 10th term is zero, then find its common difference.

The nth term of an A.P. is given by,

a_n = a + (n - 1)d.    (Eq 1)

Given , a = -18 and a₁₀ = 0.

Putting a = -18, a₁₀ = 0 and n = 10 in Eq 1 we get,

⇒ a_n = a + (n - 1)d
⇒ 0 = -18 + (10 - 1)d
⇒ 0 = -18 + 9d
⇒ 9d = 18
⇒ d = 2.

Hence, the common difference of A.P. is 2.