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Re: A geometric sequence is a sequence in which each [#permalink]
23 Apr 2013, 21:04

2

This post received KUDOS

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Difficulty:

35% (medium)

Question Stats:

55% (01:50) correct
44% (00:29) wrong based on 67 sessions

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}

Re: A geometric sequence is a sequence in which each [#permalink]
25 Apr 2013, 02:56

Expert's post

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