If the 9^{th} term of an A.P. is zero,then th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given tha

Vedclass · Accepted Answer

$2:1$

Vedclass · Answer

(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given that the $9^{th}$ term is zero:$a_9 = a + (9 - 1)d = 0$$a + 8d = 0 \Rightarrow a = -8d$.Now,we need to find the ratio of the $29^{th}$ term to the $19^{th}$ term:$a_{29} = a + 28d = -8d + 28d = 20d$.$a_{19} = a + 18d = -8d + 18d = 10d$.Ratio $= \frac{a_{29}}{a_{19}} = \frac{20d}{10d} = \frac{2}{1}$.Thus,the ratio is $2:1$.

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

Similar Questions

If $a_1, a_2, \dots, a_n$ are in $A.P.$ with common difference $d$,then the sum of the following series is $\sin d (\csc a_1 \csc a_2 + \csc a_2 \csc a_3 + \dots + \csc a_{n-1} \csc a_n)$

If twice the $11^{th}$ term of an $A.P.$ is equal to $7$ times of its $21^{st}$ term,then its $25^{th}$ term is equal to

The sum of the first five terms of the series $3 + 4\frac{1}{2} + 6\frac{3}{4} + \dots$ will be

If $x, y, z$ are in $A.P.$ and $\tan^{-1} x, \tan^{-1} y, \tan^{-1} z$ are also in another $A.P.$,then:

The sum of the first three terms of a $G.P.$ is to the sum of the first six terms as $125: 152$. Find the common ratio of the $G.P.$ (in $/5$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module