If the p^{th},q^{th},and r^{th} terms of a ge | vedclass

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

Question

(B) Let the first term of the geometric progression be $A$ and the common ratio be $R$. Given that the $p^{th}$,$q^{th}$,and $r^{th}$ terms are $a, b,

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Let the first term of the geometric progression be $A$ and the common ratio be $R$. Given that the $p^{th}$,$q^{th}$,and $r^{th}$ terms are $a, b, c$ respectively,we have: $a = AR^{p-1}$,$b = AR^{q-1}$,and $c = AR^{r-1}$. Now,consider the expression $a^{q-r} \cdot b^{r-p} \cdot c^{p-q}$: $= (AR^{p-1})^{q-r} \cdot (AR^{q-1})^{r-p} \cdot (AR^{r-1})^{p-q}$ $= A^{(q-r) + (r-p) + (p-q)} \cdot R^{(p-1)(q-r) + (q-1)(r-p) + (r-1)(p-q)}$ $= A^0 \cdot R^{(pq - pr - q + r) + (qr - qp - r + p) + (rp - rq - p + q)}$ $= 1 \cdot R^0 = 1$.

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a geometric progression are $a, b, c$ respectively,then $a^{q-r} \cdot b^{r-p} \cdot c^{p-q} = \dots\dots$

Similar Questions

The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in $G.P.$ is

Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \ldots, \frac{a_{10}}{2^9}$ be a $G$.$P$. with common ratio $r = \frac{1}{\sqrt{2}}$. If $a_1 + a_2 + \ldots + a_{10} = 62$, then $a_1$ is equal to:

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,then the value of $a^{q - r} b^{r - p} c^{p - q}$ is equal to

In a geometric progression,the first term is $1$. If $4T_2 + 5T_3$ is minimum,then what is the common ratio?

Evaluate $\sum\limits_{k = 1}^{11} {\left( {2 + {3^k}} \right)} $

Vedclass Test Series

Exam Paper Generator

Online Exam Module