If 9^{th} term of an A.P. be zero, then ratio of its 29^{th} and 19^{th} term is

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8. Sequences and Series

easy

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

A

$1:2$

B

$2:1$

C

$1:3$

D

$3:1$

Solution

(b) Given that ${9^{th}}$ term $ = a + (9 – 1)d = 0$

$ \Rightarrow a + 8d = 0$

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}$.

Standard 11

Mathematics

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