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

If the $p^{th}$ term of an $A.P.$ is $q$ and the $q^{th}$ term is $p,$ then its $r^{th}$ term is

In a $G.P.$,the first term is $7$,the last term is $448$,and the sum is $889$. Find the common ratio.

After inserting $n$ arithmetic means $(A.M.s)$ between $2$ and $38$,the sum of the resulting progression is $200$. The value of $n$ is

If $1^2 + 2^2 + 3^2 + \dots + 2009^2 = (2009)(335)(4019)$ and $(1)(2009) + 2(2008) + 3(2007) + \dots + 2009(1) = (2009)(335)(x)$,then $x$ is equal to:

If the first term of a $G.P.$ $a_1, a_2, a_3, \dots$ is unity such that $4a_2 + 5a_3$ is least, then the common ratio of the $G.P.$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module