Question

The first and the last terms of a G.P. are $a$ and $k$ respectively. If the number of terms be $n$, Find ,$n-\frac{\log k-\log a}{\log r}$, where $r$ is the common ratio.

Answer 1

a,k are first and last terms of G.P.

$k=a{r}^{n-1}\log k=\log a+(n-1)\log r\log k-\log a=(n-1)\log r\frac{\log k-\log a}{\log r}=n-1n-\frac{\log k-\log a}{\log r}=1$