The 5 th and the 31 s t terms of an arithmetic progression are, respectively 1 and – 77 . If the K t h term of the given arithmetic progression is – 17 , then the value of K is

Step-by-step solution

The fifth term is 1 . So, a + 4 d = 1 The 31 s t term is - 77 . So, a + 30 d   = - 77 ⇒ 26   d   = - 78 ⇒ d = - 3    ⇒ a = 13 t k = - 17 ⇒   a + k - 1 d = - 17 ⇒ 13 + k - 1 - 3 = - 17 ⇒ - 3 k = - 33   ⇒ k = 11