If 7 times the 7^{th} term of an A.P. is equa | vedclass

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

Question

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

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) Let $a$ be the first term and $d$ be the common difference of an $A.P.$The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Therefore,$a_7 = a + 6d$ and $a_{11} = a + 10d$.According to the problem,$7a_7 = 11a_{11}$.Substituting the values,we get $7(a + 6d) = 11(a + 10d)$.Expanding both sides: $7a + 42d = 11a + 110d$.Rearranging the terms: $7a - 11a = 110d - 42d$.$-4a = 68d$,which simplifies to $a = -17d$ (Equation $1$).We need to find the $18^{th}$ term,$a_{18} = a + 17d$.Substituting $a = -17d$ from Equation $1$ into the expression for $a_{18}$:$a_{18} = -17d + 17d = 0$.Thus,the $18^{th}$ term of the $A.P.$ is $0$.

If $7$ times the $7^{th}$ term of an $A.P.$ is equal to $11$ times its $11^{th}$ term,then the $18^{th}$ term of the $A.P.$ is

Similar Questions

$\left[\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\cdots+\frac{1}{99 \times 100}\right]$ is equal to

The sum to $n$ terms of the series $2^2 + 4^2 + 6^2 + \dots$ is

If in an infinite $G.P.$ the first term is equal to twice the sum of the remaining terms,then its common ratio is

Harmonic mean of the roots of the equation $(5 + \sqrt{2})x^2 - (4 + \sqrt{5})x + 8 + 2\sqrt{5} = 0$ is:

If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0$ are in $A.P.$,then $\alpha$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module