Question

If 9^th term of an A.P. is zero, then its 29^th and 19^th terms are in the ratio ______.

Answer 1

If 9^th term of an A.P. is zero, then its 29^th and 19^th terms are in the ratio 2 : 1.

Explanation:

Let the AP have first term a and common difference d.

The nth term is T_n = a + (n – 1)d.

T₉ = a + 8d = 0

⇒ a = –8d

Then T₂₉ = a + 28d

= –8d + 28d 

= 20d

And T₁₉ = a + 18d

= –8d + 18d 

= 10d

So T₂₉ : T₁₉ = 20d : 10d = 2 : 1 (for a nonzero d).