SOLUTION: If x, y and z are consecutive terms in a geometric sequence, then y over z is equal to z over y. Show that the following numbers are consecutively in a geometric sequence:
A) 5,
Algebra.Com
Question 1052696: If x, y and z are consecutive terms in a geometric sequence, then y over z is equal to z over y. Show that the following numbers are consecutively in a geometric sequence:
A) 5, square root of 35 and 7
B) a, square root of ab and b
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If x, y and z are consecutive terms in a geometric sequence, then y over z is equal to z over y. Show that the following numbers are consecutively in a geometric sequence:
A) 5, square root of 35 and 7
r = sqrt(35)/5
r = 7/sqrt(35) = 7*sqrt(35)/35 = sqrt(35)/5
Since the ratios are the same, the sequence is geometric.
-----------------------------------
B) a, square root of ab and b
r = sqrt(ab)/a
r = b/sqrt(ab) = b*sqrt(ab)/ab = sqrt(ab)/a
Since the ratios are the same, the sequence is geometric.
-----
Cheers,
Stan H.
------------
RELATED QUESTIONS
if x, y, and z are the first three terms of a geometric sequence, show that x^2, y^2 and... (answered by mananth)
The xth, yth, and zth terms of a sequence are X,Y,Z respectively. Show that if the... (answered by KMST)
The xth, yth, and zth terms of a sequence are X,Y,Z respectively. Show that if the... (answered by AnlytcPhil,Edwin McCravy)
if x, y, and z are consecutive multiples of 5 counting from samller to largest then, what (answered by jim_thompson5910)
how to solve this system
x+y+z=28
x^2+y^2+z^2=336
Were x,y,z are terms of... (answered by mouk)
Given that {{{1/(y-x)}}} , {{{1/(2y)}}} and {{{1/(y-z)}}} are consecutive terms of an... (answered by KMST)
Suppose T is equal to x over y and R is equal to w over z, show that xz plus yw all over... (answered by Fombitz)
x, y and z are consecutive multiples of 5, counting from smallest to largest. What is x + (answered by MRperkins)
If x, y, and z are reall numbers, use the Cauchy-Schwarz inequality to show that... (answered by venugopalramana)