SOLUTION: Suppose x, y, z is a geometric sequence with common ratio r and x≠ y. If x, 2y, 3z is an arithmetic sequence, then what is r^2?

Algebra.Com
Question 1064175: Suppose x, y, z is a geometric sequence with common ratio r and x≠ y. If x, 2y, 3z is an arithmetic sequence, then what is r^2?
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
I will only give you a HINT, leaving the solution to you.


HINT 1.  Since x, y ans z form Geom.progression, y = rx and z = r^2*x.       (1)


HINT 2.  Since x, 2y and 3z form Arithm.progression, 2y-x = 3z - 2y.         (2)


HINT 3.  Having this, substitute (1) to (2).  You will get an equation


2(r*x) -x = 3(r^2*x) - 2*(r*x).


Cancel x in both sides and solve for "r".

Happy solving !!



RELATED QUESTIONS

5;x;y is an arithmetic sequence and x;y;81 is a geometric sequence.All terms in the... (answered by htmentor)
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)
Please help me this question If A,B,C and X,Y,Z are are two arithmetic sequence,then (answered by jim_thompson5910)
The first two terms of a geometric sequence and an arithmetic sequence are the same. The... (answered by Edwin McCravy)
Find the 11th term of an arithmetic sequence whose first term is 3x + y and whose common... (answered by ikleyn)
2;x;y are the first 3 terms of an arithmetic sequence . If each term is decreased by 1,... (answered by richwmiller)
When the terms of a Geometric Progression(G.P) with common ratio r=2 is added to the... (answered by greenestamps,jim_thompson5910)
Find the 21st term of an arithmetic sequence whose first term is 9x and whose common... (answered by mananth)