(A) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term is given by $a_n = a + (n-1)d$.According to the problem,$100 \times

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

(A) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term is given by $a_n = a + (n-1)d$.According to the problem,$100 \times a_{100} = 50 \times a_{50}$.$100(a + 99d) = 50(a + 49d)$.Dividing by $50$,we get $2(a + 99d) = a + 49d$.$2a + 198d = a + 49d$.$a = 49d - 198d = -149d$.The $150^{th}$ term is $a_{150} = a + 149d$.Substituting $a = -149d$,we get $a_{150} = -149d + 149d = 0$.

Class 11 Mathematics Sequences and Series Arithmetic progression

Medium

If $100$ times the $100^{th}$ term of an Arithmetic Progression with a non-zero common difference is equal to $50$ times its $50^{th}$ term,then what is its $150^{th}$ term?

A
$0$
B
$-150$
C
$150$ times its $50^{th}$ term
D
$150$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Sequences and Series

Subtopic

Arithmetic progression

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$,then the product of its middle two terms is

MediumJEE MAIN 2023

View Solution

The sum of the numbers between $100$ and $1000$ which are divisible by $9$ is:

Easy

View Solution

Let $a, b, c$ and $d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750 \beta$,then the value of $\beta$ is

DifficultJEE MAIN 2023

View Solution

If the sum of $n$ terms of an $A.P.$ is $3n^{2} + 5n$ and its $m^{\text{th}}$ term is $164$,find the value of $m$.

Medium

View Solution

If the ratio of the sum of $n$ terms of two $A.P.s$ is $(7n + 1):(4n + 27)$,then the ratio of their $11^{th}$ terms is:

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $100$ times the $100^{th}$ term of an Arithmetic Progression with a non-zero common difference is equal to $50$ times its $50^{th}$ term,then what is its $150^{th}$ term?

Similar Questions

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$,then the product of its middle two terms is

The sum of the numbers between $100$ and $1000$ which are divisible by $9$ is:

Let $a, b, c$ and $d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750 \beta$,then the value of $\beta$ is

If the sum of $n$ terms of an $A.P.$ is $3n^{2} + 5n$ and its $m^{\text{th}}$ term is $164$,find the value of $m$.

If the ratio of the sum of $n$ terms of two $A.P.s$ is $(7n + 1):(4n + 27)$,then the ratio of their $11^{th}$ terms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module