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A geometric sequence is a sequence in which each term after the first
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23 Apr 2013, 21:04
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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
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Re: A geometric sequence is a sequence in which each term after the first
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23 Apr 2013, 22:21
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
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Re: A geometric sequence is a sequence in which each term after the first
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25 Apr 2013, 02:56
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
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Re: A geometric sequence is a sequence in which each term after the first
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14 Jan 2015, 19:36
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



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Re: A geometric sequence is a sequence in which each term after the first
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05 Jul 2017, 05:17
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.



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Re: geometric sequence
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19 Mar 2020, 07:46
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Re: geometric sequence
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