The first and last terms of a G.P. are a and | vedclass

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

Question

(D) The $n^{th}$ term of a $G.P.$ is given by the formula $l = a r^{n-1}$,where $a$ is the first term,$r$ is the common ratio,and $l$ is the last term

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The $n^{th}$ term of a $G.P.$ is given by the formula $l = a r^{n-1}$,where $a$ is the first term,$r$ is the common ratio,and $l$ is the last term.Dividing both sides by $a$,we get $\frac{l}{a} = r^{n-1}$.Taking the logarithm on both sides,we have $\log\left(\frac{l}{a}\right) = \log(r^{n-1})$.Using the property $\log(x/y) = \log x - \log y$ and $\log(x^k) = k \log x$,we get $\log l - \log a = (n-1) \log r$.Rearranging the terms to solve for $n$,we get $n-1 = \frac{\log l - \log a}{\log r}$.Therefore,$n = 1 + \frac{\log l - \log a}{\log r}$.

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

Similar Questions

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

If $\sum_{i = 1}^n \sum_{j = 1}^i \sum_{k = 1}^j 1 = 560$,then the value of $n$ is:

The interior angles of a polygon are in $A.P.$ If the smallest angle is $120^{\circ}$ and the common difference is $5^{\circ}$,then the number of sides is

The sum $11^{2} + 12^{2} + \cdots + 20^{2} + 21^{2} = ?$

If $f(x + y, x - y) = xy$,then the arithmetic mean of $f(x, y)$ and $f(y, x)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module