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

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(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

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