Question

16.

If the 9th term of an A.P. is zero, then the ratio
of its 29th and 19th term is
​

Answer 1

Answer:-

Given:

9th term of an AP = 0

we know that,

nth term of an AP – a(n) = a + (n - 1)d.

Hence,

→ a + (9 - 1)d = 0

→ a + 8d = 0

→ a = - 8d -- equation (1)

We have to find:

Ratio of its 29th term and 19th term.

Now,

→ a(29) = a + (29 - 1)d

Substitute the value of a from equation (1).

→ a(29) = - 8d + 28d

→ a(29) = 20d

a(19) = a + (19 - 1)d

→ a(19) = - 8d + 18d

→ a(19) = 10d

Hence,

→ a(29) : a(19) = 20d : 10d

→ a(29) : a(19) = 2 : 1

Therefore, the ratio of 29th term and 19th term of the given AP is 2 : 1.