Question

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

Answer 1

The given AP is 21, 18, 15,...

First term, a = 21

Common difference, d = 18 – 21 = –3

Suppose n^th term of the given AP is –81. then,

a_n = –81

⇒ 21 + (n – 1) × (–3) = –81   ...[a_n = a + (n – 1)d] 

⇒ –3(n – 1) = –81 – 21 = –102

⇒  `n - 1 = 102/3 = 34`

⇒ n = 34 + 1 = 35

Hence, the 35th term of the given AP is –81.