Question

the 8/9th term of A.P is zero prove that its 29th term is divisible its 19th term

Answer 1

Let first term be a,common difference be d.
Given.9th term is zero.
therefore , a + (9 - 1)d =0 ,--> a + 8d =0 ....(1)
19th term = T19= a + (19 -1)d =a + 18d = -8d + 18d =10d ( a = -8d from eqn. (1) ).
Similarly, T29 =a + (29 -1 )d= a + 28d =
= -8d +28d =20d
therefore, T19 = 10d and T29 = 20d
Here we can simply see that T29 = 2 times of T19, 29th term is divisible by 19th term.