If the 19^{th} term of a non-zero A.P. is zer | vedclass

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

Question

(C) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term of an $A.P.$ is given by $t_n = a + (n-1)d$.Given that the $19^{th}$

Vedclass · Accepted Answer

$3 : 1$

Vedclass · Answer

(C) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term of an $A.P.$ is given by $t_n = a + (n-1)d$.Given that the $19^{th}$ term is zero: $t_{19} = a + 18d = 0$,which implies $a = -18d$.We need to find the ratio $\frac{t_{49}}{t_{29}}$.$t_{49} = a + 48d = -18d + 48d = 30d$.$t_{29} = a + 28d = -18d + 28d = 10d$.Therefore,the ratio is $\frac{30d}{10d} = \frac{3}{1}$,which is $3 : 1$.

If the $19^{th}$ term of a non-zero $A.P.$ is zero,then the ratio of its ($49^{th}$ term) to ($29^{th}$ term) is:

Similar Questions

If $a$ and $b$ are two numbers,$A$ is the arithmetic mean,and $S$ is the sum of $n$ arithmetic means between $a$ and $b$,then what does $S/A$ depend on?

If $a^2, b^2, c^2$ are in $A.P.$,then $(b + c)^{-1}, (c + a)^{-1}$ and $(a + b)^{-1}$ will be in

If $a_1, a_2, a_3, \dots, a_n$ are in $A.P.$ and $a_1 + a_4 + a_7 + \dots + a_{16} = 114$,then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

If the sum of $n$ terms of an $A.P.$ is $3n^2 + 5n$ and $T_m = 164$,then $m = $

If the $m^{th}$ terms of the sequences $63, 65, 67, 69, \dots$ and $3, 10, 17, 24, \dots$ are equal,then $m = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module