Question

Which term of the AP 21, 18, 15,...is −81?
(a) 25th
(b) 18th
(c) 35th
(d) 46th

Answer 1

(c) 35^th
In the given AP, we have a = 21 and d = (18 - 21) = -3
Let the n^th term be -81.
Then a_n = -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 35^th terms is -81.