Question

If \(\color{green}{pth \; , \; \color{blue}{qth}}\) and \(\color{red}{rth}\) terms of a \(\color{green}{\mathbf{G} \text{eometric} \; \mathbf{P} \text{rogression}}\) be : \(\color{blue}{a, b}\) and \(\color{blue}{c}\) respectively, then:

the value of :

\[\color{green}{\large (a^{q -r} \times b^{r-p} \times c^{p-q}) } \; \; is :\]

\(\color{red}{Answer \; : \; 1}\)

Answer 1

is it \[\frac{ab}{c^2}\]

Answer 2

yes,i am getting 1 :)

Answer 3

Please explain @hartnn

Answer 4

lol...its \[1\]

Answer 5

let F be 1st term,R be common ratio....a=F*R^(p-1),similarly,b,c....question asked can be expressed as (a/c)^q*(b/a)^r*(c/a)^p.....(a/c)^q=R^(pq-rq)......adding all powers of R we get 0,so ans=1......sorry i m not good at explaining neatly with cool pics :P

Answer 6

I show you clearly what @hartnn meant.

\[\large pth \; term = A \cdot r^{p-1} \implies a = A \cdot r^{p-1}\]
\[\large qth \; term = A \cdot r^{q-1} \implies b = A \cdot r^{q-1}\]
\[\large rth \; term = A \cdot r^{r-1} \implies a = A \cdot r^{r-1}\]

\[a^{q -r} \times b^{r-p} \times c^{p-q} \implies A^{(q-r +r-p+p-q)} \cdot r^{(p-1)(q-r)+(q-1)(r-p)+(r-1)(p-q)}\]

\[\implies A^{0} \cdot r^{(pq -pr -q + r +rq -pq -r + p + pr -rq -p + q)} \implies A^{0} \cdot r^{0}\]

\[\implies (1) \cdot(1) = 1\]

Answer 7

how to write like that?...not using draw......using equation??how?

Answer 8

Using equation button..

Answer 9

i was trying to write upon sign...like a/c...how do i make a and c show in different line with dash in between?

Answer 10

Like:

\[\frac{a}{c}\]

Answer 11

??

Answer 12

yes,how u did that?

Answer 13

\frac{}{}

Answer 14

In equation editor write;

frac{}{}

brackets must be these only..

numerator will in first bracket and denominator will be in second one..

frac{a}{c}

Answer 15

i have to write { then f then r then a....no shortcut??

Answer 16

I mean it is a code..

Answer 17

\[\frac{a}{c}\]

Answer 18

hmmmm....tedious :P

Answer 19

Great..

Can you write this : a/b/c/d ??

Answer 20

\[\frac{a}{b}{c}{d}\]

Answer 21

I wish I could give you more medals for this..

Ha ha ha..

Answer 22

frac{a}{b}{c}{d} doesn't work....

Answer 23

It won't

You can use {}{} two times only not 4 times..

Answer 24

\[\frac{\frac{a}{b}}{\frac{c}{d}}\]

Answer 25

frac{frac{}{}{frac{}{}} worked :)

Answer 26

Yes it will..

Great work..

Now one I thing I must do for you..

Answer 27

\[\huge \color{green}{\textbf{Welcome To The World Of Latex..}}\]

Answer 28

oh,so this is latex!heard about it.....

Answer 29

@hartnn If you want to learn LATEX then you can post your question here :

http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)

Answer 30

ohh!!separate latex group......'LATEXIANS'... :P

Answer 31

Yes..