Question

if 9 term of ap is zero prove that it's 29 term is doubled the 19 term

Answer 1

In A.P the first term� = a and common difference = d. Given that� 9th term of an A.P. is 0. Therefore t9 = 0 ⇒ a + 8d = 0 ⇒ a = -8d� --------------(1) We have to prove that t29 = 2 t19. t19 = a + 18d = -8d + 18d = 10d������� [� from (1) ] t29� = a + 28d = -8d + 28d = 20d������� [� from (1) ] t29� = 2 x 10d = 2 x t19 ∴ t29� = 2 x t19