If a, b, c are the p^{th}, q^{th} and r^{th} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the first term of the $G.P.$ be $A$ and the common ratio be $R$.Then,$a = A R^{p-1}$,$b = A R^{q-1}$,and $c = A R^{r-1}$.Substituting these in

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the first term of the $G.P.$ be $A$ and the common ratio be $R$.Then,$a = A R^{p-1}$,$b = A R^{q-1}$,and $c = A R^{r-1}$.Substituting these into the expression:$\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q = \left( \frac{A R^{r-1}}{A R^{q-1}} \right)^p \left( \frac{A R^{q-1}}{A R^{p-1}} \right)^r \left( \frac{A R^{p-1}}{A R^{r-1}} \right)^q$$= (R^{r-q})^p (R^{q-p})^r (R^{p-r})^q$$= R^{pr - pq + qr - pr + pq - qr}$$= R^0 = 1$.

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

Similar Questions

The value of $(2 \cdot {}^{1}P_{0} - 3 \cdot {}^{2}P_{1} + 4 \cdot {}^{3}P_{2} - \dots$ up to $51^{\text{th}}$ term) + $(1! - 2! + 3! - \dots$ up to $51^{\text{th}}$ term) is equal to

$\sqrt {\underbrace {111........1}_{200\,digits} - \underbrace {222.......2}_{100\,digits}} $ equals :-

If $\log_3 2, \log_3(2^x - 5)$ and $\log_3(2^x - 7/2)$ are in $A.P.$,then $x$ is equal to

Determine $k,$ so that $k+2, 4k-6$ and $3k-2$ are three consecutive terms of an $A.P.$

If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module