Question

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

Answer 1

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