Question

If the 9th term of an A.P.be zero, then the ratio of
its 29th and 19th term is-
(A) 1:2 (B) 2:1 (C) 1:3 (D) 3:1

plz give answer with method .....plz help me fast I need it ....plz
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Answer 1

Answer:

B) 2 : 1

Step-by-step explanation:

Here,

9th term is zero as given.

So,

T9 = a + ( 9 - 1 ) d

0 = a + 8d

a = - 8d.. (1)

We have to find the ratio of it's 29th and 19th term.

T19 = a + ( 19 - 1 ) d

= a + 18d

= -8d + 18d .. ( from 1 )

= 10d

Now,

T29 = a + ( 29 - 1 ) d

= -8d + 28d

= 20d

Now,

T29 / T19 = 20d / 10d

= 2 / 1

Thus, Ratio of T29 and T19,

T29 : T19 = 2 : 1

Thus, B) 2 : 1 is the answer.

Answer 2

Answer: b) 2:1

Step-by-step explanation:

a = first term of an AP

As we know,

In an AP for any nth term,

Tn = a + ( n - 1 ) d

∴ 9th term = a + (n-1)d

                = a + (9-1)d

                 = a + 8d

From above, a = -8d

∵  29th term = a + 28d

    19th term = a + 18d

On putting the value of a,

29th term = (-8d )+ 28d

                    = 20d

19th term = a + 18d

                =(-8d) + 18d

               = 10d

hence, The ratio of 29th term and 19th terms is

⇒$\frac{20d}{10d}$

⇒$\frac{2}{1}$

⇒ 2: 1