Question

if the 9 th term of an A.P. is 0. Then proove that its 29 th term is double than the 19 th term.​

Answer 1

Answer:

True

Step-by-step explanation:

In APs nth term is given by a + ( n - 1 )d, where a is the first term and d is the common difference.

Let in this AP first term be a and common difference be d.

Here,

  9th term = 0

⇒ a + ( 9 - 1 )d = 0

⇒ a + 8d = 0    ⇒ a = - 8d

   19th term

⇒ a + ( 19 - 1 )d = a + 18d

   From above, a = - 8d

⇒ - 8d + 18d

⇒ 10d

   29th term

⇒ a + ( 29 - 1 )d

    From above, a = - 8d

⇒ - 8d + 28d

⇒ 20d

              ⇒ 20d = 2 * 10d  ⇒ 29th term = 2 * 19th term

Proved.