Let 2^{text{nd}},8^{text{th}},and 44^{text{th | vedclass

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

Question

(D) Let the first term of the $A.P.$ be $a = 1$ and the common difference be $d$.The $2^{	ext{nd}}$,$8^{	ext{th}}$,and $44^{	ext{th}}$ terms are $1

Vedclass · Accepted Answer

$970$

Vedclass · Answer

(D) Let the first term of the $A.P.$ be $a = 1$ and the common difference be $d$.The $2^{	ext{nd}}$,$8^{	ext{th}}$,and $44^{	ext{th}}$ terms are $1+d$,$1+7d$,and $1+43d$ respectively.Since these terms are in $G.P.$,we have $(1+7d)^2 = (1+d)(1+43d)$.Expanding both sides: $1 + 49d^2 + 14d = 1 + 44d + 43d^2$.Simplifying: $6d^2 - 30d = 0$,which gives $6d(d - 5) = 0$.Since the $A.P.$ is non-constant,$d 
eq 0$,so $d = 5$.The sum of the first $20$ terms $S_{20} = \frac{20}{2}[2(1) + (20-1)5]$.$S_{20} = 10[2 + 95] = 10 	imes 97 = 970$.

Let $2^{\text{nd}}$,$8^{\text{th}}$,and $44^{\text{th}}$ terms of a non-constant $A.P.$ be respectively the $1^{\text{st}}$,$2^{\text{nd}}$,and $3^{\text{rd}}$ terms of a $G.P.$ If the first term of the $A.P.$ is $1$,then the sum of the first $20$ terms is equal to:

Similar Questions

If $m$ is the $A.M.$ of two distinct real numbers $l$ and $n$ $(l, n > 1)$ and $G_1, G_2, G_3$ are three geometric means between $l$ and $n$,then $G_1^4 + 2G_2^4 + G_3^4$ equals:

Let $a_n = \frac{10^n}{n!}$ for $n = 1, 2, 3, \ldots$. Then the greatest value of $n$ for which $a_n$ is the greatest is

Let $a_i = i + \frac{1}{i}$ for $i = 1, 2, \ldots, 20$. Let $p = \frac{1}{20} \sum_{i=1}^{20} a_i$ and $q = \frac{1}{20} \sum_{i=1}^{20} \frac{1}{a_i}$. Then,

If $t_n$ is the $n^{th}$ term of an arithmetic progression and $t_7 = 9$,what is the value of the common difference $d$ that minimizes the product $t_1 t_2 t_7$?

If $a, b, c$ are in $G.P.$ and $\log a - \log 2b, \log 2b - \log 3c$ and $\log 3c - \log a$ are in $A.P.$,then $a, b, c$ are the lengths of the sides of a triangle which is

Vedclass Test Series

Exam Paper Generator

Online Exam Module