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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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66% (01:17) correct 34% (01:18) wrong based on 140 sessions
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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. p-3, r-3, s-3, t-3, u-3
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: an-arithmetic-sequence-is-a-sequence-in-which-each-term-59035.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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19 Mar 2020, 07:46
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