logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
0 votes

If the $ i^{th},j^{th}\; and\; k^{th} $ term of an AP and a GP are equal and are $x,y,z$ find the value of $x^{(y-z)}\;.y^{(z-x)}\;.z^{(x-y)}$

$\begin{array}{1 1} xyz \\ \large\frac{x+y+z}{2} \\ 1 \\ (x-y)(y-z)(z-x) \end{array}$

Can you answer this question?
 
 

1 Answer

0 votes
Answer : (c) 1
Explanation :
$x=a+(i-1)d=b\;r^{i-1}$
$y=a+(j-1)d=b\;r^{j-1}$
$z=a+(k-1)d=b\;r^{k-1}$
$x-y=(i-j)\;d$
$y-z=(j-k)\;d$
$z-x=(k-i)\;d$
$x^{y-z}\;.y^{z-x}\;.z^{x-y}= [b\;r^{(i-1)}]^{(j-k)d}\;. [b\;r^{(j-1)}]^{(k-i)d}\;. [b\;r^{(k-1)}]^{(i-j)d}$
$b^{(j-k+k-i+i-j)d}\;.r^{(i-1)(j-k)+(j-1)(k-i)+(k-1)(i-j)d}$
$=b^{0*d}\; r^{0*d}=(br)^0=1.$
answered Jan 2, 2014 by yamini.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...