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Re: A geometric sequence is a sequence in which each [#permalink]

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23 Apr 2013, 21:04

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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 \(\sqrt{r}\)

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

Re: A geometric sequence is a sequence in which each [#permalink]

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14 Jan 2015, 08:36

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