Question

If the 9^th term of an A.P. is zero, then find the ratio of its 29^th term to its 19^th term.

• A. 1 : 2
• B. 2 : 1
• C. 1 : 3
• D. 3 : 1

Answer 1

The correct option is B

2 : 1

Given that the 9^th term = 0 $\Rightarrow a+(9-1)d=0$
$\Rightarrow a+8d=0$
Now,
29^th term = $a+(29-1)d=a+28d$
19^th term = $a+(19-1)d=a+18d$
So, the ratio of 29^th and 19^th terms $=\frac{a+28d}{a+18d}=\frac{(a+8d)+20d}{(a+8d)+10d}=\frac{20d}{10d}=\frac{2}{1}.$