Which term of the AP 21, 18, 15, ... is - 81?

In the given AP, the first term = a = 21

Common difference = d = 18 - 21 = - 3

To find: place of the term - 81.

So, let a_n = - 81

Since, we know that

a_n = a + (n - 1) × d

∴ - 81 = 21 + (n - 1) × (-3)

⇒ - 81 - 21 = - 3n + 3

⇒ - 102 = - 3n + 3

⇒ - 102 - 3 = - 3n

⇒ - 3n = - 105

⇒ n = 105/3

⇒ n = 35

∴ 35^th term of the AP is - 81.