(D) The $n^{th}$ term of a $G.P.$ is given by $l = a r^{n-1}$.Dividing both sides by $a$,we get $\frac{l}{a} = r^{n-1}$.Taking the logarithm on both s

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$1 + \frac{\log l - \log a}{\log r}$

(D) The $n^{th}$ term of a $G.P.$ is given by $l = a r^{n-1}$.Dividing both sides by $a$,we get $\frac{l}{a} = r^{n-1}$.Taking the logarithm on both sides,we have $\log(\frac{l}{a}) = \log(r^{n-1})$.Using the properties of logarithms,$\log l - \log a = (n-1) \log r$.Therefore,$n-1 = \frac{\log l - \log a}{\log r}$.Adding $1$ to both sides,we get $n = 1 + \frac{\log l - \log a}{\log r}$.

Class 11 Mathematics Sequences and Series Geometric progression

Easy

The first and last terms of a $G.P.$ are $a$ and $l$ respectively; $r$ being its common ratio; then the number of terms in this $G.P.$ is

A
$\frac{\log l - \log a}{\log r}$
B
$1 - \frac{\log l - \log a}{\log r}$
C
$\frac{\log a - \log l}{\log r}$
D
$1 + \frac{\log l - \log a}{\log r}$

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Sequences and Series

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Geometric progression

If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

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If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,then the value of $a^{q - r} b^{r - p} c^{p - q}$ is equal to

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If $S_n$ is the sum of $n$ terms of a geometric progression with first term $a$ and common ratio $r$,what is the sum of $S_1 + S_3 + S_5 + \dots + S_{2n-1}$?

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Six positive numbers are in $GP$,such that their product is $1000$. If the fourth term is $1$,then the last term is

MediumWBJEE 2013

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For a $G.P.$,if $(m+n)^{\text{th}}$ term is $p$ and $(m-n)^{\text{th}}$ term is $q$,then the $m^{\text{th}}$ term is $.........$

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The first and last terms of a $G.P.$ are $a$ and $l$ respectively; $r$ being its common ratio; then the number of terms in this $G.P.$ is

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