If the common difference of an A.P. is -3 and the 18th term is -5, then find its first term.

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

a_n = a + (n - 1)d.    (Eq 1)

Given , d = -3 and a₁₈ = -5.

Putting d = -3, a₁₈ = -5 and n = 18 in Eq 1 we get,

⇒ a_n = a + (n - 1)d
⇒ -5 = a + (18 - 1)(-3)
⇒ -5 = a + 17 × (-3)
⇒ -5 = a - 51
⇒ a = 51 - 5
⇒ a = 46.

Hence, the first term of A.P. is 46.