The ratio of the 7^{th} to the 3^{rd} term of | vedclass

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

Question

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

Vedclass · Accepted Answer

$10:3$

Vedclass · Answer

(D) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given that the ratio of the $7^{th}$ term to the $3^{rd}$ term is $12:5$:$\frac{a + 6d}{a + 2d} = \frac{12}{5}$Cross-multiplying gives:$5(a + 6d) = 12(a + 2d)$$5a + 30d = 12a + 24d$$30d - 24d = 12a - 5a$$6d = 7a$$a = \frac{6}{7}d$Now,we need to find the ratio of the $13^{th}$ term to the $4^{th}$ term:$\frac{a_{13}}{a_4} = \frac{a + 12d}{a + 3d}$Substituting $a = \frac{6}{7}d$ into the expression:$\frac{\frac{6}{7}d + 12d}{\frac{6}{7}d + 3d} = \frac{\frac{6d + 84d}{7}}{\frac{6d + 21d}{7}} = \frac{90d}{27d} = \frac{90}{27}$Simplifying the fraction by dividing by $9$:$\frac{90}{27} = \frac{10}{3}$Thus,the ratio is $10:3$.

The ratio of the $7^{th}$ to the $3^{rd}$ term of an $A.P.$ is $12:5$. Find the ratio of the $13^{th}$ to the $4^{th}$ term.

Similar Questions

Find the sum of $\left(1-\frac{1}{n+1}\right)+\left(1-\frac{2}{n+1}\right)+\left(1-\frac{3}{n+1}\right)+\cdots+\left(1-\frac{n}{n+1}\right)$

If $H$ is the harmonic mean between $p$ and $q$,then the value of $\frac{H}{p} + \frac{H}{q}$ is

If the ratio of the sum of the first three terms and the sum of the first six terms of a $G.P.$ is $125 : 152$,then the common ratio $r$ is:

If ${A_1}, {A_2}$; ${G_1}, {G_2}$ and ${H_1}, {H_2}$ are $AMs$,$GMs$,and $HMs$ between two quantities,then the value of $\frac{{G_1 G_2}}{{H_1 H_2}}$ is

Sum the series to infinity $\frac{3}{4} - \frac{5}{4^2} + \frac{3}{4^3} - \frac{5}{4^4} + \frac{3}{4^5} - \frac{5}{4^6} + \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module