If {a_1}, {a_2}, {a_3}, dots, {a_n}, dots are | vedclass

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

Question

(C) Let $r$ be the common ratio of the $G$.$P$. Then ${a_n} = {a_1}{r^{n-1}}$.Taking logarithm on both sides,we get $\log {a_n} = \log {a_1} + (n-1)\l

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) Let $r$ be the common ratio of the $G$.$P$. Then ${a_n} = {a_1}{r^{n-1}}$.Taking logarithm on both sides,we get $\log {a_n} = \log {a_1} + (n-1)\log r$.Let $A = \log {a_1}$ and $R = \log r$. Then $\log {a_n} = A + (n-1)R$.Now,the terms in the determinant are of the form $\log {a_{n+k}} = A + (n+k-1)R$.Applying column operations ${C_2} 	o {C_2} - {C_1}$ and ${C_3} 	o {C_3} - {C_2}$:${C_2} - {C_1}$ results in entries: $(n+2-1)R - (n-1)R = 2R$,$(n+8-1)R - (n+6-1)R = 2R$,and $(n+14-1)R - (n+12-1)R = 2R$.${C_3} - {C_2}$ results in entries: $(n+4-1)R - (n+2-1)R = 2R$,$(n+10-1)R - (n+8-1)R = 2R$,and $(n+16-1)R - (n+14-1)R = 2R$.Since columns ${C_2}$ and ${C_3}$ become identical (both consist of $2R$),the value of the determinant $\Delta = 0$.

Similar Questions

Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If
$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$
then the value of $\lambda^{2}$ is equal to $.....$

Without expanding,prove that $\Delta = \begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix} = 0$.

$\left| {\begin{array}{ccc} 1/a & a^2 & bc \\ 1/b & b^2 & ca \\ 1/c & c^2 & ab \end{array}} \right| = $

By using properties of determinants,show that:
$\left|\begin{array}{ccc}x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4\end{array}\right|=(5x+4)(4-x)^{2}$

Let $D_{k} = \begin{vmatrix} 1 & 2k & 2k-1 \\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix}$. If $\sum_{k=1}^{n} D_{k} = 96$,then $n$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module