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 of the $A.P.$ 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 tha

Vedclass · Accepted Answer

$3 : 1$

Vedclass · Answer

(C) 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 $t_n = a + (n - 1)d$.Given that the $19^{th}$ term is zero,we have $t_{19} = a + 18d = 0$,which implies $a = -18d$.We need to find the ratio of the $49^{th}$ term to the $29^{th}$ term:$\frac{t_{49}}{t_{29}} = \frac{a + 48d}{a + 28d}$.Substituting $a = -18d$ into the expression:$\frac{t_{49}}{t_{29}} = \frac{-18d + 48d}{-18d + 28d} = \frac{30d}{10d} = 3$.Thus,the ratio 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

The interior angles of an $n$-sided convex polygon are in $G.P.$ The smallest angle is $120^\circ$ and the common ratio is $2$. Find the number of possible values of $n$.

If $a, b, c$ are in $GP$ and $4a, 5b, 4c$ are in $AP$ such that $a + b + c = 70$,then the value of $a^3 + b^3 + c^3$ is

Let $n (> 1)$ be a positive integer. Then,the largest integer $m$ such that $(n^m + 1)$ divides $(1 + n + n^2 + \dots + n^{127})$ is:

If $a, b, c, d, e, f$ are in $A.P.$,then the value of $e - c$ will be

If the sum of an infinite $G.P.$ is $9$ and the sum of the first two terms is $5$,then the common ratio is

Vedclass Test Series

Exam Paper Generator

Online Exam Module