Question

If pth, qth and rth terms of a G.P. are x, y, z respectively, then write the value of $x^{q-r}{y}^{x-p}{z}^{p-q}$.

Answer 1

$a_p=x=a{r}^{p-1}$ ............ (i)

$a_q=y=a{r}^{q-1}$ ............ (ii)

$a_r=z=a{r}^{r-1}$ ............ (iii)

$X^{q-r}{y}^{r-p}{Z}^{p-q}$

$=\left[q{r}^{p-1}{]}^{q-r}\right[a{r}^{q-1}{]}^{r-p}[a{r}^{r-1}{]}^{p-q}$

$=a^{q-r+r-p+q}{r}^{pq-pr-q+r+qr-p+q}$

$=a^0{r}^0$

$=1$

$x^{q-r}\times y^{r-p}\times z^{p-q}=1$