Author 
Message 
TAGS:

Hide Tags

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 583

Re: A geometric sequence is a sequence in which each
[#permalink]
Show Tags
23 Apr 2013, 22:04
Question Stats:
66% (01:17) correct 34% (01:21) wrong based on 220 sessions
HideShow timer Statistics
rakeshd347 wrote: v, w, x, y, z A geometric sequence is a sequence in which each term after the first is equal to the product of the preceding term and a constant. If the list of numbers shown above is an geometric sequence, which of the following must also be a geometric sequence?
I. 2v, 2w, 2x, 2y, 2z II. v + 2, w + 2, x + 2, y + 2, z + 2 III.\sqrt{v}, \sqrt{w}, \sqrt{x},\sqrt{y}, \sqrt{z}
(A) I only (B) II only (C) III only (D) I and II (E) I and III
KUDOS please if you like my question. We know that v,w,x,y,z are in GP. Thus, w/v = x/w = y/x = z/y = r(some constant, called the common ratio) I. A multiplication by a constant (2) will not change the ratio, as evident. III. The ratio for these terms will be another constant \(\sqrt{r}\) E.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Manager
Joined: 04 Mar 2013
Posts: 57
Location: India
Concentration: Strategy, Operations
GPA: 3.66
WE: Operations (Manufacturing)

Re: A geometric sequence is a sequence in which each
[#permalink]
Show Tags
23 Apr 2013, 23:21
Can be done quite easily if 4 nos are considered instead of the variables For example 1, 2, 4, 8 I multiply 2 : 2, 4, 8, 16 ; they are still in GP II Add 2: 3, 4, 6, 10 ; not in GP III Square root : 1, \sqrt{2}, 2, 2\sqrt{2} ; still in GP So clearly I and III i.e E is the correct answer
_________________
When you feel like giving up, remember why you held on for so long in the first place.



Math Expert
Joined: 02 Sep 2009
Posts: 59588

Re: A geometric sequence is a sequence in which each
[#permalink]
Show Tags
25 Apr 2013, 03:56
rakeshd347 wrote: v, w, x, y, z
A geometric sequence is a sequence in which each term after the
first is equal to the product of the preceding term and a constant. If the list of numbers shown above is an geometric sequence, which of the following must also be a geometric sequence?
I. 2v, 2w, 2x, 2y, 2z II. v + 2, w + 2, x + 2, y + 2, z + 2 III. \(\sqrt{v}\), \(\sqrt{w}\), \(\sqrt{x}\), \(\sqrt{y}\), \(\sqrt{z}\)
(A) I only (B) II only (C) III only (D) I and II (E) I and III Similar question from OG13: Quote: p, r, s, t, u
An arithmetic sequence is a sequence in which each term after the first term is equal to the sum of the preceding term and a constant. If the list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?
I. 2p, 2r, 2s, 2t, 2u II. p3, r3, s3, t3, u3 III. p^2, r^2, s^2, t^2, u^2
(A) I only (B) II only (C) III only (D) I and II (E) II and III Discussed here: anarithmeticsequenceisasequenceinwhicheachterm59035.html
_________________



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A geometric sequence is a sequence in which each
[#permalink]
Show Tags
14 Jan 2015, 20:36
I. 2v, 2w, 2x, 2y, 2z
Multiplication by 2 keeps the GP sequence intact
II. v + 2, w + 2, x + 2, y + 2, z + 2
Addition breaks the GP sequence in this case
III.\(\sqrt{v}, \sqrt{w}, \sqrt{x},\sqrt{y}, \sqrt{z}\)
Square rooting is nothing but changing the power from 1 to \(\frac{1}{2}\) ; it still keeps the GP sequence intact
Answer = E



Director
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

A geometric sequence is a sequence in which each
[#permalink]
Show Tags
05 Jul 2017, 06:17
mau5 wrote: rakeshd347 wrote: v, w, x, y, z A geometric sequence is a sequence in which each term after the first is equal to the product of the preceding term and a constant. If the list of numbers shown above is an geometric sequence, which of the following must also be a geometric sequence?
I. 2v, 2w, 2x, 2y, 2z II. v + 2, w + 2, x + 2, y + 2, z + 2 III.\sqrt{v}, \sqrt{w}, \sqrt{x},\sqrt{y}, \sqrt{z}
(A) I only (B) II only (C) III only (D) I and II (E) I and III
KUDOS please if you like my question. We know that v,w,x,y,z are in GP. Thus, w/v = x/w = y/x = z/y = r(some constant, called the common ratio) I. A multiplication by a constant (2) will not change the ratio, as evident. III. The ratio for these terms will be another constant \(\sqrt{r}\) E. Let the common ratio of the terms in GP be r. So, w = vr x = vr^2 y = vr^3 z = vr^4 Now lets start checking I , II & III I. 2v, 2w, 2x, 2y, 2z = 2v, 2vr, 2vr^2, 2vr^3, 2vr^4 Common ratio = r. So, GP II. (v+2), (w+2), (x+2), (y+2), (z+2) = 2v+2, 2vr+2, 2vr^2 +2 , 2vr^3 +2, 2vr^4 +2 . Not in GP. III. \(\sqrt{v},\sqrt{w},\sqrt{x},\sqrt{y},\sqrt{z}, = \sqrt{2v}, \sqrt{2vr}, \sqrt{2vr^2},\sqrt{2vr^3},\sqrt{2vr^4}\) Common ration = \(\sqrt{r}\). So, GP Answer E.




A geometric sequence is a sequence in which each
[#permalink]
05 Jul 2017, 06:17






