(c) 35th
In the given AP, we have a = 21 and d = (18 - 21) = -3
Let the nth term be -81.
Then an = -81
⇒ -81 = a + (n - 1)d
⇒ -81= 21 + (n - 1) ⨯ (-3)
⇒ -81 = 21 - 3n + 3
⇒ -81 = 24 - 3n
⇒ -81 - 24 = -3n
⇒ -105 = -3n
⇒ 3n = 105
⇒ n = 35
Hence, the 35th terms is -81.