Question

If x, y , z be respectively the pth, qth and rth terms of G .P., then $(q-r)\log x+(r-p)\log y+(p-q)\log z=$

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

The correct option is A $0$

Let first and common ratio of G.P are $a$ and $r$ respectively
$T_p=a{r}^{p-1}=x$
$\log x=\log a+(p-1)\log r$
Similarly write $\log y$, $\log z$
Multiply by $q-r$, $r-p$ and $p-q$ and add we get,
$(q-r)\log x+(r-p)\log y+(p-q)\log z=0$