Question

If a, b, c are $p^{th}$, $q^{th}$, and $r^{th}$ terms of a G.P., then $\left(\frac{c}{b}{)}^p\right(\frac{b}{a}{)}^r(\frac{a}{c}{)}^q$ is equal to

• A. 1
• B. $a^p{b}^q{c}^r$
• C. $a^q{b}^r{c}^p$
• D. $a^r{b}^p{c}^q$

Answer 1

The correct option is A

1

a = $A{R}^{p-1}$, b = $A{R}^{q-1}$, c = $A{R}^{r-1}$

$\therefore \left(\frac{c}{b}{)}^p\right(\frac{b}{a}{)}^r(\frac{a}{c}{)}^q$ = $\left(\frac{A{R}^{p-1}}{A{R}^{q-1}}{)}^p\right(\frac{A{R}^{q-1}}{A{R}^{p-1}}{)}^r(\frac{A{R}^{p-1}}{A{R}^{r-1}}{)}^q$

= $R^{(r-q)p+(q-p)r+(p-r)q}$ = $R^0$ = 1